I don't understand why your mom doesn't just give in on the house. I have two kids and I am not advocating this on any other matter but they can nag me so much I give in to things I would normally say no to.

You could buy a really large crate to keep her in while your not home at least she would be out of the elements. Convince your mom you would bathe her weekly.

I know you have tried all of this but now that the law is involved maybe she will budge.