Kiedyś będziecie musieć sprzedać ten samochód - souds tottaly odd! should be: Kiedyś będziecie musieli sprzedać ten samochód.
Why wouldn't this work?
"Kiedyś będziecie musiały ten samochód sprzedać"
Does it sound weird?
It's possible, but it's not the usual word order. You rather put the verb first and then its object.
Is there a reason why musieć isn't accepted?
I think the first comments make this clear. For the "polish ears" two infinitives sound bad.
Not sure what happens if three are needed, though :) But perhaps in regular speech they aren't.
The singular form of you is not acceptable here? Kiedyś będzie musiał sprzedać ten samochód.
Everything is fine with this sentence, but it's in 3rd person: "he will have to sell". You missed the -sz in "będziesz".
I think there is a bug in this new 'fill in the gap' format. I wrote Kiedyś and checked several times!
Why not: Kiedyś będziesz musieli sprzedać ten samochód?
"będziesz" is 2nd person singular ... but "musieli" is plural ... so that doesn't fit together.