I would personally go the "tough love" route before I sent off a baby to another home... Nahla is just a puppy & tried using the screaming bit when she had to go into her ex-pen. Sometimes you just have to put your foot down and show them how it's going to be. If you give in once they will know from that point on all they have to do is cry til you give in again.
Buuut I know sometimes it goes deeper than that. Some dogs can experience severe separation anxiety and get themselves all worked up over it... I don't know much about it but I have heard of people using mood stabilizers, like doggie paxil or something.
If it's really a problem maybe consult your vet before re-homing.