Hi Nancy. We live in the suburbs with an unfenced yard. Our grandchildren ages 6 and 9 visit us frequently and play in the yard. Our neighbor with an unfenced yard tells us he is getting a put bull.
If you had grandchildren ages 6 and 9 who played in your unfenced yard and your next door neighbor with an unfenced yard told you he was getting a pit bull, would you be concerned? We do have the grandchildren and the neighbor.
It seems like a lot of your letter is missing, but here's the answer to your question:
If the pit is a puppy, just have your grandchildren make friends with it. Unless the dog is mistreated, they usually love children.
If the neighbor is getting a rescue and you don't know if it was abused or not, then have your neighbor bring the dog first to you without your grand kids to see how the dog reacts. If it seems very friendly to you, then on ANOTHER day have him bring the dog over with your grand kids there. Watch the dog carefully, BUT NOT FEARFULLY, his reaction to the children. Have your neighbor keep him on the leash durng all introductions. As I say, unless they are not used to children or have been abused, they normally are a wonderful children's dog. It wouldn't hurt for the children to have treats each time they see the dog. Once a relationship is established, the pit is quite loyal to it's friends. In fact, it could be protective to a degree if someone is aggressive toward your grandchildren.
If the dog seems extremely nervous around the children it probably is not used to being around them. That could present a problem if the children are overly frind.ly. You should explain to them that this dog is not used to children and that they must go very slow. If they pet the dog for awhile each time they see it, the pit will also be won over. Even a great dog that has not been around children can be nervous which could lead to a problem.
Just take it slow. Do not feel aggressive or defensive around a pit. Just be calm and they respond to that with a lot of respect and love. They also like to come to you, so you can be available, but don't force the issues. They are a terrier after all. lol. They love to be talked to in a slightly higher voice, it usually melts them.
ps I have raised all kinds of terriers, never pits, I like the small crowd, myself