Congrats to your mother for being a responsible dog owner! People everywhere could stand to take a page from her book. I just hope she knows that even if the dog is socialized very well with other dogs, when it reaches maturity, it still may not end up liking other dogs. It just happens, and it can be controlled, but that part of their history is very ingrained.
I know of my two, my gamebred (I'm not a fighter, I mean gamebred like what she is supposed to look like, not a freakishly large pit)girl, Gabby, picks and chooses which dogs she likes, but my younger, Kaya, "bully style" who is "purebred" from a backyard breeder, loves all dogs, and wets herself around cats. It all depends on the dog, but just a word of caution. Something tells me if your mother is doing the puppy classes she may already know all this, but just in case.
It gets a lot of people when their dog, no matter the breed, reaches about 2 and seems to change overnight when it comes to other dogs and also their territory. They don't sometimes realize that it's a completely natural thing that happens, much like puberty for us. I know when I was that age I was a terror.
That is the best thing you can do. Get the dog socialized around people and other pets early and frequently. But as solosmoke mentioned, bully breeds can be very stubborn and will test your 'pack' leadership. Around 2-3 is likely the last big push. Just don't let the dog be dominant and you shouldn't have any problems. What you describe is just likle the bully breeds - naturally friendly to people. Also, spaying or neutering at a young age also helps with behavior issues when done early.