Yoda-English again? "We move from Amerlca to Hungary" is rejected. Why not "To Hungary move to America we" then? (Reported if course).
Because then there would be two "to"'s in the sentence. :)
Anyway, this is probably a closer translation:
"We move to Hungary from America."
For "We move from America to Hungary", I would say "Amerikából Magyarországra költözünk."
But these are tiny differences, your version should certainly be accepted, along with Yoda's.
Looks like the original problem has been fixed, but I think this would be better in present progressive: "We are moving..". unless the speaker moves from the US to Hungary on a regular basis. Which I guess is possible, but less likely than just moving once.
In the vast majority of these translations, without a specific context, the present progressive is a much more natural translation.