Good grief!
The OP has already said that this is less about the money than the way in which her partner has treated her by referring to the ex in the way he did.
Nowhere has she said (or implied) that she is jealous of the ex herself, or that she wants to interfere in the present-giving setup.
I'm not sure how anyone on here can judge about meanness or otherwise, as these things are so subjective, and vary from family to family.
Without knowing more about the relationships it's impossible to know, but it could be that the ex is often used as triangulation - ie as a third party who is quoted and compared with the OP as a way of making her feel insecure or inadequate. That sort of thing can be subtle, and it can take a long time to realise that it's happening, as it's easy to think that you are being unreasonable, or over-reacting, particularly if it is part of a bigger picture.
If that is what's happening here, and the OP has just realised, she will be confused, and being told to keep out of it and all the other snide remarks will be the last thing she needs. And words fail me about the rent and tax comment!