My mother is selfish and inconsiderate and isn't willing to back off when asked.
So you recognise this is bad behaviour
She lets her feelings get the better of her and suffers from verbal diahorrea which leads to thoughtless comments.
She makes thoughtless comments. She should learn to control her behaviour. But actually it sounds like people get her away with it, so she doesn't
She was very loving and caring when bringing me up and is always offering to help.
What did she actually do, beyond the basics of bringing up a child?
You've mentioned a lot of negative things about her. Are you saying this because you feel you ought to?
She makes me feel I'm the only one with a key to her happiness as 'family is everything'.
Not fair on you.
I resent the fact she never made more effort to move on from my dad and I am effectively her emotional support. Perhaps I have enabled this but it's just kind of happened since I was too young to know not to.
And certainly not fair on a child
My wife is being very hard-nosed about it all but I was never a new mother and don't know how much damage it has really done, so I have to take her at face value that my mother causes her mental health to suffer.
I don't think it's anything to do with being a new mother - it's more to do with not having experienced a family relationship with a person who was "loving and caring" - you claim your mother is that - do you think the way she treated your wife was loving and caring?
I also feel she makes ultimatum-like statements when we discuss this which are unkind when I am just trying to work through a problem.
I agree. But equally I suspect the bi-monthly visits are your wife's compromise and she actually finds even that too much
I don't like that my wife is unprepared to attempt to improve the situation.
So what would need to happen for the situation to improve? For example, would it help if your mother apologised for past behaviour and demonstrated she had changed? Would she do this, or does she not think she has anything to apologise for?
I don't care what happens to me, I just want a compromise that everyone can make peace with and doesn't affect my daughter's happiness (ie doesn't break up my family - I was a child of divorce and I don't ever want that for her).
For this, and for every other one of the points OP, I would really suggest you have therapy to help you understand yourself, and your family dynamics. I found this post incredibly sad. You have spent your whole life pleasing others - first your mum, and now your wife, to the point it seems that you have lost your whole identity. Best of luck.