Why won’t my neighbor allow her kids to come over inside our home to play with my kids but I allow mine to go inside their house? These kids have been friends now for well over a year.
Since I don’t know your neighbor, all I can do is guess at some reasons.
Maybe they are overprotective
Maybe they have trust issues
Maybe they are afraid you have guns in your house
Maybe they don’t like you but do like your children.
Maybe one of the parents is a control freak.
Maybe they are afraid their child will make a mess at your house or break something.
The only way to know for sure is to ask them. Granted, they might not want to talk to you, but at least you tried.
Invite the mother over for tea or coffee when the kids are at school and invite her children over for a supervised play date. Invite her to come as well. If she declines, ask her if she could explain why… did you do something to offend her? You might get some answers that way.