Our daughter has a pit bull...only he thinks he’s a little lap dog. The kids sit on him, play dress-up with him, pull his ears and tail, and he just takes it. He is the best dog ever. They got him from another military family that could not take him to their next duty station, he was a rescue dog that had been trainined to fight but would’nt.
This is not a breed thing, it’s an owner thing. My grandma had the meanest dog ever...a snappy little poodle.
When it does jump the fence or break free to get at a passing dog and its owners; your daughter's “lap dog” will think it is doing its duty to protect its area, and it will attack and potentially kill.
You and your family had better hope that the day never comes when that animal decides he has had enough or feels provoked in some way. It is a breed thing.