First here are some of the possible syntax/meaning combinations based on your example, with main phrasal stress highlighted in bold:
mihi est fīlius decōrus "I have a handsome son" (typical topic-comment)
est mihi fīlius decōrus (presentational, a combination of "there is" and "I have")
fīlius decōrus mihi est "my son is handsome = I have a handsome son, don't I?" (narrow-focus); or "what I have is a handsome son" (broad-focus). These two would be distinguished by intonation.
fīlius mihi decōrus "a son whom I consider handsome"
fīlius decōrus meus "my handsome son" (last-word stress here sounds analytically definitional)
fīlius (meus) decōrus est (meus) "my son is handsome"
fīlius decōrus meus est "the handsome son is mine"
fīlius decōrus meus est "my handsome son exists" (sounds rather strange)
fīlius meus mihi decōrus est "my son is handsome to me"
mihi meus fīlius decōrus est "to me, my son is hansome"
And here are some generalisations that can be drawn from these and other examples:
- The Dative mihi belongs to the verb, forming the compound predicate mihi est. By default, it answers the question quid tibi est? "what do you have (there)?" and cannot appear without a verb being at least implied.
- Unless it forms a compound predicate with est, the adjective meus belongs to the noun, forming the noun phrase fīlius meus. It answers the question cuijus fīlius "whose son?" or quis "who?", and like any noun phrase can appear without a verb.
- The compound predicate mihi est literally means "he exists in relation to me" and conveys the person who experiences or is affected by the existence of the subject. The experiencer is in the center of the relation, and the translation is often "I have", but not necessarily, e.g. nūlla spēs est mihi "I don't expect/hope for anything". Possibly the underlying relation is locative, or otherwise spatial.
- The compound predicate meus est means "he's mine (as opposed to yours)", and puts the owned subject in the center.
- Datives are used with many other verbs to express indirect object (mihi dīcitur "it's being said to me"), experiencer (mihi vidētur "it seems to me"), locative possessor (mihi inventus est/aufūgit "I found him/he escaped from me"), but in none of these uses can it be conceivably replaced with the adjective meus. No ambiguity of choice exists with verbs other than est + abest & de(e)st.
- When mihi modifies an adjective/adverb, they form a predication relation: mihi decōrus is equivalent to quī mihi decōrus est "who to me is handsome, whom I feel to be handsome". Normally the Dative immediately preceeds the adj./adv., but it can be fronted for emphasis ("if you ask me").
- English has some remnants of the same use of the Dative (most IE languages do; in some it's still fully productive, e.g. Slavic) - for example who is he to you? English speakers are likely to be thrown off by the fact that the normal answer to this question in English is the counterintuitive he's my son, whereas the parallel he's a son to me talks instead about a metaphorical father-son relationship. English has a strange obsession with possessive pronouns, which are even used instead of articles: wave your hand ("right, I was about to wave yours"), buy your bread from us ("is this a ransom?").
- Even so, I'll never be a wife to you can mean the same as I'll never be your wife, although what it really means is "I'm not going to perform the role of a wife for you".
- Finally there's fīlī mī, a noun phrase with something that looks like a Dative, and that's what it started out as in all likelyhood (the original short clitic form of mihi, a contrast still found in e.g. Serbo-Croatian). However by the historical stage its function became that of the Vocative, and that's how it's described by most grammars. The feminine equivalent is said to be mea, but in fact mī is attested with feminines too, although rarely.
- Seeing as in the Spanish mi hijo, mi nieta the proclitic mi always comes before the noun, it's probably unrelated, but simply a reduced form of the full pronouns mio, mia (which come after), parallel to the proclitic-only su "his/her".
Keep in mind that these generalisations won't replace acquiring the correct use of these constructions naturally through encountering and understanding them in context.