The i in videt is short. The length of a vowel in classical Latin pronunciation is defined by its duration—its "quantity"—as opposed to its "quality", i.e. the nature of the sound: its waveform or timbre. But first let's have a look at short-vowel quality, since that seems to be the focus of your question. Then we'll come back to rhythm and hopefully it will all make sense.
Phonetic pressure on short vowels
Sidney Allen, in Vox Latina, says "in the case of the close and mid vowels (i and u, e and o) the long appear to have been appreciably closer than the short." That is, the tongue is higher ("closer" to the roof of the mouth) in the long forms of these vowels. (See chapter 2 for details about the evidence for this.)
However, the quality of the long vowel was felt to be the primary "nature" of the vowel. If you asked a Roman to clearly make the sound of I, you would hear ī, not ĭ. The reason that Roman speakers gave the short vowel a distinct quality was not to distinguish the short vowel from the long vowel—the rhythm did that—but because of phonetic pressure. Since a short vowel is said very quickly, there is a natural tendency not to lift the tongue as high as when the vowel gets its "full" duration. This is why a is unaffected: the tongue is low ("open") in the long vowel. The change in vowel quality in the short forms of the other vowels is just a weaker kind of vowel reduction—the tendency, seen in English and sometimes in German, to pronounce short unstressed vowels as a schwa.
Since the change in vowel quality is due to phonetic pressure from the preceding and following phonemes and the short time for the vowel, we should expect that the quality doesn't change in all contexts. Indeed Sidney Allen reports that in diēs, the short i had the same quality as long ī. This is because before e, there is no phonetic pressure to alter the quality of ĭ.
From all this, I understand that when a vowel is short, the long and short qualities are heard as allophones—perceived as the same vowel. So, it's perfectly fine to use the long-vowel quality in a short vowel. In fact, I think it's wise for a beginner to do this. The long quality is the perceptual anchor, and beginners should start by burning in the perceptual anchors. You can make your pronunciation more lax when you've mastered it—but see below for why you might never want to.
Rhythm is fundamental
When you say pater et māter, the syllables should come out in this rhythm:
♪♪♩ ♩ ♩
The syllables are: pă-tĕ-rĕt-mā-tĕr. Ørberg will explain this, but not until chapter 34. It's worth knowing right when you begin, because mastering the rhythm of a language early makes it easier to learn.
Similarly, Mārcus nōn videt Quīntum should have this rhythm, regardless of the quality that you give the short i's:
♩ ♩ ♩ ♪♩ ♩ ♩
That might be a good one to practice, because the only short syllable is vĭ-.
Quis mē vocat? has this rhythm:
♩ ♩ ♪♩
Ørberg will hit you with some minimal pairs distinguished only by vowel length, too, like malum (bad, evil) and mālum (apple).
When you're speaking in the classical Latin rhythm, you will feel the phonetic pressure to pronounce ĕ, ĭ, ŏ, ŭ in a slightly lax manner. Then you will probably give in to that pressure without intending to. You don't need to do it on purpose.
Reconstructed Classical Pronunciation ≠ ancient Roman pronunciation
If you read Vox Latina or any scholarly treatment of ancient Roman speech, you will find all sorts of ways that pronunciation varied from spelling. The m in final -am, -em, -im, -om, -um was not pronounced, and the vowel was nasalized; a final vowel was often dropped when the next word started with a vowel, so Iūlia Aemiliam vocat could be pronounced Iūli' Aemiliam vocat—this is called "elision"; censor was actually pronounced cẽsor (with a nasalized e); fīliī was pronounced fīlī, at least in some centuries; Marcus and many others dropped the h in homō; calidus was pronounced caldus; and many more. But of course not everyone pronounced Latin that way; in a cosmopolitan empire of 60,000,000 people spread from Portus Cale to Ægyptus, lasting 1,200 years, there are going to be some variations in pronunciation—many of which were never documented.
Unless you are particularly interested in reproducing Roman colloquial speech, I don't think you need to worry about any of that if you're learning Reconstructed Classical Pronunciation. Reconstructed Classical Pronunciation is a modern pronunciation of Latin, just like the Italian pronunciation of Latin, the French pronunciation of Latin, the Slavic pronunciation of Latin, and all the rest. RCP is a somewhat artificial pronunciation, just as classical Latin was a somewhat artificial language. Unlike the others, RCP approximates the rhythm of classical Latin, as well as its segmental phonemes—passably well. Since the year 800, Latin has been defined by its writing, with various local standards for pronunciation, which enabled people to understand each other's speech—passably well. RCP is just one more post-800 pronunciation standard, but it's worldwide rather than local. Many people speak RCP and don't even bother with vowel quantity.
So, I conclude that it's OK to make your speech supremely clear by always using the long vowel quality even in short vowels. Catullus might mock you for it, but Catullus is long gone. If you master the rhythm, though, you'll be able to perceive the poetry. Googling for a videt in the Aeneid turned this up (Book I, line 128):
Disiectam Aeneae toto videt aequore classem.
He sees Aeneas's fleet scattered all over the sea.
which scans like this—requiring vĭ- to be short:
Dis-iec/t⁐Ae-nē/ae tō/tō vi-de/tae-quo-re / clas-sem.
If you don't follow that, wait until you finish Chapter 34.