I'm sorry you have to make this decision :(
We have 2 small dogs, one is very placid, the other very boisterous. My 16 month old DD plays happily with both under supervision, I trust them but generally do not leave her alone with them. I've also noticed she started off very gentle with them but as her confidence is growing, she's getting more rough with them. If either ever snapped, they'd be gone in a flash but until them, I trust them.
However, my dh owned 2 staghounds that he used purely for hunting. Around the farm they were beautiful placid dogs but if you ever saw one of them attack while hunting, my lord. There is a switch and you would not know they were the same dogs fetching a ball for us 5 minutes earlier. That's their instinct, that's their nature and that's their bloodline. I could never ever have those dogs around my children so they had to go, I guess I see staffy's and pitbulls in the same light unfortunately, something could just click and if it did, could you ever forgive yourself?
Fwiw, I would not take my child to a house where there was a pitbull, I would not trust the dog and I would not trust my child to be gentle enough to be safe :(

