Is it your B that is starting it? They usually do not howl/"bark" for very long- certainly it would not be the entire time you were away. How long do they dogs bark for when you leave?
Have you talked with your neighbors to explain your situation? If they bark at like 7 or 8pm, then I think your neighbors can be irritated with it, but certainly not mad. But if it's like at 2 in the morning, and your neighbors are constantly getting woken up– then there's a real problem.
Do you have anyone who could stay at your place to keep the kids calm?
As I'm understanding your post- it's just a temporary thing- 3 months, right?
If worse comes to worst- you could always board them somewhere, although that would be a very expensive alternative. I agree about the bark collar-- One of our friends had one for their dog and it was so sad. It really changed her personality. And the two times I tried a shock collar on my B, it had horrible effects. The B did not know what in the heck was happening and it just scared her pretty badly. Not a good idea for Bs, IMO.
What else could you try? Are they crated? What breed are the other dogs? Are their "sitters" that do over nights? I still think having a friend stay at your place might be the best option...