Well, I have a GSD and speaking from my dog encyclopedia and my own experience, they are not so great with other dogs. My friend has a Lasa Aphso named Rusty and he is a purebred, but close enough. He gets along fine with his house-mate, Jessie, who is even a female! I wouldn't give up after the first try, dogs are very protected and usually will not do well at the first meeting. I have and will never bring Lady to my friend's house because she is a 75 pound dog and he is like 10 pounds (as you mentioned before, big difference). If you still want to try and get them to get along try and bring them to a place where neither of them is on their own territory, like a park that neither of them never visit or something. Also, you and your mom should just try and stay as much out of the way as possible except to hold the leash (obviously). That is just my suggestion though.