Yes, Be2 is the best move to play against both Qe6+ and Qe5+. There are a few reasons for this:
1) Be2 does not block any of your Kingside pieces from developing, allowing you to castle quickly and then attack Black's misplaced Queen. While Be2 does block one of your pieces (your White Queen on d1), this is fine because you shouldn't be developing the Queen early anyways.
2) Be2 does not allow Black to exchange their misplaced Queen off. This allows you to use the Black Queen as a tempo-gainer (i.e., later in the game you can develop your pieces with tempo by attacking it). If you played Qe2 instead of Be2, it would give Black an opportunity to get rid of their bad Black Queen.