If your mom signed a contract when she got your first dog, that the dog would be kept inside, I'm sorry to say this, but they can take that dog away. It's called a breach of contract.
The local resuce organization here goes through a lot to match up a dog with the right home. My neighbors adopted a dog from them last year, and had to sign a ton of papers. When we adopted Abbey from the Beagle rescue, it was the same thing.

I can't imagine leaving my dogs outside all the time. Yes, my yard is fenced, and totally secured, but I want them in here with me because they are my family.
I don't understand why anyone would even want to get a dog if they want to leave it outisde all the time. That is a concept totally lost on me.

I don't think the shelter you were at did anything wrong--they do have the dog's best intentions at heart, and that's what is important.