D.B.
You don't really have a friendship anymore - you just have some habitual get-togethers. I don't think you have to do anything dramatic - just decline the invitation. You don't have to say you have something else planned, if she will take offense at you having scheduled something on a day you know to be his birthday. Just say that you are sorry your son will not be able to attend but you wish the child a happy birthday. I wouldn't even send a card - that just encourages a continuation of the contact. Just let this friendship drift away. If she says anything to you, you can say that the kids have grown in different directions and don't seem to enjoy each other the way they once did, that your son has quite naturally formed friendships with kids in his class, as has her son. THen stop issuing invitations from your end. Send a holiday card if you want but that's it.
Her little digs at you are based on her own insecurities about NOT working outside the home, and since she can't make herself feel better, she tries to make you feel like less of a person. Try to feel compassion for her but don't try to change her or convince her of your abilities or priorities. It will make things worse and end things on such a negative note.
This is not like breaking up with a boyfriend where you really have to say "I don't like you anymore" - your circumstances are such that you won't see each other unless you specifically arrange it. So just don't arrange it! You don't want a big confrontation anyway, so just let this slide away, cherish the memories of what you had for some years, and keep those in your mind.
I did this with friends of ours and it has worked out so much better. That way, when we did cross paths, it wasn't uncomfortable.