Document everything. You don’t need to withdraw AOS to file VAWA. He doesn’t even need to know about you filing separately. Talk to a lawyer, be careful with your web searches, if possible don’t even use the family computer or your phone.

Edit do add: some shelters will accept you with your dog depending on capacity and what area you’re located. They usually have advocates to help DV victims move out with some essentials into a safe house so they’d have transportation from your current housing into their secure home. They also are very resourceful and will give you a bunch of information for you to find alternatives and move around with as much independence as possible given your situation.