I understand fully what you are going through. My seven year old son pulled down the trousers of a 3 year old little girl at a party. i was not there at the time and after I found out I,ve tried to talk to the girl's mother and she says she is too upset to talk to me. I dont know if I should write a letter of apology or what. Like you I am embarrased and dread picking up the kids from school as the girl's sister is in the same school.
From what I've heard and read kids at 7 start exploring sexually but the fact that he did with a three year old makes it hard and the fact that the parents wont talk to me makes it even harder.
So you are not alone, take heart and hopefully all will go well.
First off, you have been looking after this girl for many years as you mentioned, and have always kept watch and made sure that they were safe, so don't be too hard on yourself. This girls mother should be extremely greatful you have done so for so long. Not only that, you did the right thing by letting her mother know straight away, so give yourself some credit here.
You were very lucky that your daughter came to you and raised the alarm before anything potentially bad happened, and as you said yourself, you intervened quickly. I honestly think after talking to your son, the embarrassment of being caught might possibly be enough to not ever do it again.
I don't believe your son is a child molester, but i do believe he is on the cusp of puberty and all sorts of feelings may be taking over at the moment. It might be worth having a talk about what is/will be happening to him. Yes you try and reach out to your neighbour (i'm assuming it's the girl and mother that live next door) as you have done such a good thing over the years, and also you got through the hardest part of telling her what happened, now you need to wait for the dust to settle and then explain to her that you value them both and would like to repair what happened.
It may take some time, but time heals all wounds! good luck :)