"The small blue car is moving in between those big buses."
Translation:A kicsi kék autó azok között a nagy buszok között halad.
Any hints on when you use "kis" versus "kicsi"? ("A kis, kék kocsi ... " not accepted, suggested answer instead has "kicsi")
If it's in front of a noun, both kis and kicsi are good. If separate, you should only use kicsi.
Do you really need to say között twice? A kicsi kék autó azok a nagy buszok között halad?
Yes; if you have "this" or "that" (or "these" or "those") and the noun takes a case or a postposition, then the "this/that/these/those" needs to take that case as well: azon az asztalon "on that table", e mögött a ház mögött "behind this house", azok alatt a fák alatt "under those trees", ebben a szobában "in this room", etc.
IMHO there is no strict rule that the verb goes at the end of the sentence. Therefore "A kicsi kek auto halad azok között a buszok között" shall be accepted. Or?
would "azok között a nagy buszok között halad a kicsi kék autó" also be acceptable, or did I do something weird with the emphasis of the sentence or something?
No, your sentence is very fine and it has the same focus as the preferred Hungarian sentence.
Because Hungarian uses postpositions, which come after the things they modify.
As opposed to English which uses prepositions, which come before the things they modify.
So just as we wouldn't say "moving those busses between" but rather "moving between those busses" (with "between" in front of "those busses"), Hungarian has to have the között after the azok and the a nagy buszok.