Hi A.,
I have a similar situation with a next door neighbor, but I am on the other end. I have 2 sons, 6 and 4, and my neighbor's son is 7. I have had many issues with him coming to my house and being very mean to my 4yr old. So, let me start by saying that I really appreciate that you are acknowledging your daughter's behavior and addressing it, because my neighbor is not.
I tried many things with him, but what eventually worked (but still not every time) is that I put myself in his shoes. I started thinking that maybe it's not fair to expect the 6-7 yr olds to be able to play with a 4 yr old. So I sat him down with my boys and had a talk with them. I told them that I understand that sometimes playing with someone younger can be frustrating, but that it's never all right to be mean to him about it. So we came to an agreement that if my 4yr old starts getting on the big one's nerves, they come and tell me and I will do something else with him. I also made a no crying rule, so that if anyone starts crying, he goes home.
It doesn't help that he is not disciplined at home, but we have come a long way here. When I forget to remind him about the rules we still have problems, so I try to remind him every time that I see him. Heck, sometimes I have to remind myself not to get annoyed with some of the things that my little one does, so how can I expect a 7yr old to, but I still can't let him be mean to my son.
It is better when my older son goes to my neighbor's house, so maybe you could try having you daughter's friend come to your house. 2 yr olds are just getting started to get into everything, so it is probably really hard for your daughter to deal with that. Babies don't want to take your stuff, so she probably does fine with your niece.
So, because of my own experience, what I would say is that if the other mother can't distract the 2yr old and keep him from playing with the girls, than maybe they should play at your house and that that's OK becasue those are very hard ages to play together. It doesn't mean that there is anything wrong with your daughter or with your neighbor's son. They are just not the right ages to be playing together. And who knows, maybe in 30 years you'll be telling this story at their wedding!
Well, good luck with this situation. I'm sure that everything will work itself out OK. Sorry for writing so much.
Sincerely,
S.