I have teachers here who do that. If they complain in
private, say "I agree, and we're working on it." If they
reprimand me in public, I say "come here please, we can talk
in private."
Field trips are something you must plan very carefully. They
can't legally exclude the kid from trips, but they can do so
anyway and say it was an error. Try talking to the other
teachers about their fears and concerns with your kids going
on the trip. This should shut them up.