I hope sincerely that she's not pretending to consider what you want to get what she wants. You probably need to have a conversation in order to figure that out.
I'm wondering - what prevents you from keeping the dog once you have it? She's kept it for 3 months, why don't you keep it for 3 months now? From what I know, posession is half the law. I'd take the dog to the vet for a checkup while you have it, too, so you can get some records and other documentation in your hands.
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17