You obviously have a strong command of Latin, so I will try to address my comments to a more advanced level, even though I myself rarely operate at an advanced level in Latin.
I have recently been trying to study Latin word order specifically, as a I reactivate my generally meager Latin abilities. I have mostly studied two works of Devine and Stephens on Latin word order and pragmatics and a similar one on classical Greek word order. They have made great progress in explaining the rules of word order and pragmatics in these languages, but don't understand or explain everything. I understand their conclusions only partially, especially since I am not a formally trained linguist, so am sure of even less than what they put forward. Having been suitably warned, you can appropriately evaluate what I say below.
Here is my assessment of the principles you stated.
My understanding is that generally the adjective goes after the noun,
unless there's also a genitive for the noun in which cases the order
is: adjective, genitive, and noun.
This is one of those typical guidelines given to beginning Latin students that may be helpful as a start, but which is linguistically incorrect and misleading as to what rules really apply to Latin. The rules for basic adjective word order are actually not all that different from the rules in Spanish, and I think in Portuguese. The presence of genitives is a complicating factor, but is not governed by simple rules.
Caesari principum et optimatium solida fidelitatis pignora is the
predicative, so it goes before the verb.
It is true that typically the verb is final in Latin, but there are many, many exceptions driven by other discourse factors not discussed in almost any grammar books aimed at learners.
The dative Caesari comes first.
Again there is no such actual rule; however, the typical Latin sentence has the following order: subject, direct object, indirect object, instrumental, place, and verb. There are again constant deviations from this basic order because of other discourse factors.
principum et optimatium are genitives for solida fidelitatis pignora,
so it comes before.
The order of genitives is driven by multiple factors. The first is that the more informative word from a semantic perspective should go first and the assumed referent should go second (e.g., casus belli "case for war" or omnis spes salutis "all hope of safety"). Second, the word that is more important from a discourse perspective should go first (ut pellatur mortis et religionis metus "so that fear of death and the supernatural be eliminated"). As you can see, these factors can work in opposite directions.
solida fidelitatis pignora follows the rule I mentioned before:
adjective, genitive, and noun.
There are many times that Latin follows this order because it creates a compact noun phrase; however, it is not a syntactic rule, but rather a rule driven by subtle semantic and discourse factors.
Here is my analysis of the teacher's answer, using my stripped down understanding of Devine's and Stephens' theories and my own terminology. (Their terminology is quite complex and implicates additional linguistic theories I only partially understand and would have to explain at length.)
The syntax of Latin word order almost never determines meaning, so almost any order of the words is strictly grammatical and meaningful; however, discourse factors and semantics usually have a strong effect on the surface Latin word order, so it is far from random. Often the effects are subtle and open to stylistic variation.
The basic word order for the elements of a sentence is that the assertion at issue goes last ("the core assertion"). It is optionally preceded by whatever puts the assertion in its correct context ("the restriction"). That is optionally preceded by whatever puts the entire statement in its appropriate discourse context ("the sentence topic").
The sentences at issue in the three languages are:
The hostages of the Gauls of good family were for Caesar solid pledges
of the fidelity of the chiefs and the nobles.
Os reféns dos gauleses de boa família eram para César sólidos penhores
de fidelidade dos chefes e dos nobres.
Ingenuorum obsides Gallorum solida erant Caesari principum et
optimatium fidelitatis pignora.
The order of the English and Portuguese is driven primarily by syntax. The only words easy to move about are the phrases "for Caesar" and "para César." Why are these not at the beginning of the sentence? It is because the sentences as written treat the effect on Caesar as secondary and not important to the core assertion of the effectiveness of this tactic. The reference to Caesar is tail material belonging to the "restriction," rather than a "sentence topic." This is a stylistic choise driven by the point you want to make, not a rule of syntax. The Latin translation reflects this choice.
The sentence as a whole is meant to convey the idea that the good families will guarantee good behavior through pledges. Accordingly, the "sentence topic" is ingenuorum, the good families. In English and Portuguese, you have to start with the subject of the verbs, which are the hostages, but not in Latin.
The tactic of the good families that will be used is giving hostages, so this goes second in the genitive phrase as "ingenuorum obsides." The hostages are accommodated or guessable items in the sentence, not good sign posts of what the communication is really about.
We already know that we are in the middle of wars with the Gauls, so the mention of Gauls is mere tail material and should go last in the "sentence topic," giving "ingenuorum obsides gallorum" "The good families, who were Gauls of course, provided hostages." Although some ambiguity is possible, it doesn't really impact the discourse intention. Even in English and Portuguese, it is not completely clear if "of good family/de boa família" applies to the Gauls or the hostages. It really has to apply to both in a general way. Similarly, there is no interpretation of gallorum that would really change the overall meaning.
Next we have the predicate that might include the "core assertion," but is a different concept. In English, the intonation would reach a peak on the focused word, which would be "solid." I think I could do this with intonation in Brazilian Portuguese as well, but it might not be as obvious or as required as it would be in my American English. The teacher has realized this focus by using hyperbaton to move the word "solida" from the "core assertion" to earlier in the sentence in the "restriction." It is now a signpost to help you interpret the "core assertion" appropriately. This sentence is not meant to convey a mere formalistic transaction. It conveys that Caesar has gotten a good reason to feel at ease. Using hyperbaton, to put "solida" earlier in the "restriction" part of the sentence conveys this important extra meaning that is conveyed by intonation in English.
We now move to the rest of the "restriction," begun with "solida." It is followed by "erant" which we normally expect to be sentence final, as verbs "usually" are. However, there is a rule that forms of the copula (i.e., forms of the verb sum) tend to rise from the end of the sentence to attach themselves to the earliest word in the sentence bearing strong focus. If there is no such word, it stays in place. In this case, it "rises" to attach itself to "solida," which has strong focus in hyperbaton as I discussed before.
Next we have "for Caesar"/"para César"/"Caesari. The sentences as written in all three languages are not mainly about Caesar's attitude, but about the secureness of this type of arrangement; therefore "Caesari" is mere tail material closing the "restriction" and reminding us that Caesar will benefit from this good deal.
Now we have the "core assertion" about what is offered by the "good families," "the pledges of the fidelity of the chiefs and the nobles"/"penhores de fidelidade dos chefes e dos nobres." In English and Portuguese, the order is fixed by the syntax. For the Latin, the semantics and the discourse decides the word order. For Latin, the significant thing is actually the status of the people and not what they give. They could have given promises, money, troops, or religious vows. In deciding which to put first in the genitive construction, the special people are more informative and the pledges are easily accommodated or guessable information. Therefore, we say: principum et optimatium fidelitatis pignora with the genitive words first. We don't need to use "solida" here because it was already used in the "restriction" to restrict the applicability of the "core assertion" about pledges, and its neuter ending makes it clear that it refers to the pignora.
How does your answer work? First, it is syntactically perfect, but rather strange from a discourse perspective.
Gallorum ingenuorum obsides Caesari principum et optimatium solida
fidelitatis pignora erant.
Names of people almost always follow the noun for semantic reasons, as is true in Spanish and Portugues, so saying gallorum ingenuorum is almost as strange as saying gauleses boas famílias. It leaves you wondering what personality traits of the families seem of a Gaulish type, rather than simply indicating their nationality.
Starting with Gallorum also suggests that the sentence is meant to say how the Gauls in general reacted, whereas we already know that Gauls are involved in the war and so are just interested in knowing what the "good families" did, not the Gauls in general.
Saying solida fidelitatis pignora is grammatically correct, but strongly suggests that "solid faith pledges" are a known thing by themselves unconnected with anything else. To me, a solid faith pledge is the same thing as a pledge. In the case at hand, the fidelitatis is more a function of the attitude of the principum et optimatium, than of the things themselves, and so the genitative should tend to be associated with them, rather than with the things.
Lastly, leaving "solida" and "erant" where they are suggests that the intent of the sentence is to identify the hostages as pledges and not something else, like gifts or sacrifices, as opposed to saying that the hostages were part of a secure arrangement made by the good families and that was of benefit to Caesar.
I hope this explanation helps to flesh out this difficult and subtle topic and doesn't create more confusion. It is probably best to start to learn about the syntax and morphology of Latin first and worrying about the semantics and discourse issues later. I only decided to go to such great lengths, because the lack of similar explanation led me to turn away from what seemed the random chaos of Latin, rather than to peak my interest in the subtle manipulation of word order for rhetorical purposes.
