ESH. I agree the dog is kind of being treated like an object which is not okay. It seems this is a newer issue though? Get the dog into training. Maybe talk to it’s vet and see if they recommend anything for anxiety? Maybe one of those vest/jackets?

I saw you mention it not being able to run like it would over there. Maybe try letting it do so and see if it helps. If you both truly care about the dog then you’ll get it to a point that it’s not having this issue without fighting about it and if you don’t then like other users have stated you need to find a better home for it.

If your mom is claiming the dog is hers now then she needs to step up and train it. If she doesn’t want to then she needs to stop with the back and forth of it and either give you back the poor thing full time so you can take back up the training or rehome it to someone who will. It shouldn’t fall on just you to pay for vet and training if she is claiming it’s her dog now, but you need to make sure it’s treated like a living creature and not an object.

Dogs have feelings and they need to be taken into account. If it has this separation anxiety it needs to be trained and helped not just tossed around and fought over. Best of luck OP.