I think that is an excellent email. Since ou have to live next door to these folks, I think it is worth going out of your way to get on with them. Sounding off to them, especially in writing, is a really good way to get off to very bad start.
I know that everyone is lambasting you for being too soft, but I think exactly he opposite. If I was accused of being rude, I would buy flowers for the wife and ask forgiveness.
It's so easy to end up with bad neighbourly relationships, and so beneficial when those relationships are positive, so I think it's worth falling over yourself to get on together.