How will getting a divorce while owning real estate impact my BAH?

Ok. The Army could go one of two ways. As you would be divorced, single again and a PVT, they could say no you no longer get BAH and must move into the barracks. The other way they could go is as you are already in a house, and getting BAH, they may let you keep it but reduce your BAH to just BAH without dependents. No the animals do not count as dependents. Get with you command. No one here can really definitively answer your question.

There is an exception to policy that may be granted by the post commander to allow you to continue to receive BAH for a while

I do not recommend that you with hold the information. That would be a slippery slope that you would not recover from when caught.

Inform your command and explain the issues, likely for them to understand, for the short term. For the long term you need to think realistically how home ownership and pets workout for a single Soldier. Normal duty alone does not likely allow you to run home and take out the pets, the same is true when you have assigned duty’s overnight, or longer training periods. All of it costs money, money that a private does kit usually have. I am sure you do not wish to neglect your pets.

Bottom line speak to the command, request that they waiver and look for a more reasonable permanent solution.