I've come back to this because, on reflection, some really simple messages bear repeating:
Firstly, one of the simplest, most effective but oft overlooked bits of relationship advice ever: You do not need to understand how somebody else is feeling, in order to believe that they feel that way. All you need to do is recognise that they are a person in their own right, not an extension of you and, listen to what they tell you, extending them the everyday courtesy of believing what they tell you about themselves.
Secondly, especially given the difficult early weeks, it's very possible that your wife might have post-natal depression. It can kick in later, even if not present at the start. It's worth encouraging her to talk to a doctor about this, just to check she's ok and get any help needed.
Thirdly, when you marry, you commit to put your spouse at the centre of your world and to live your lives as partners, working together, always listening to the other and showing them kindness and patience. Of course you maintain family and other relationships too but they become less central as a you form a couple and it is impossible for anyone else to occupy the 'centre of your world' position that your spouse does. How therefore, can you possibly think of your mother as occupying that central position in your life, competing for it with your wife?
That is what your 'rock and a hard place' comment implies. That you have positioned your mother at the centre of your universe, alongside your wife. Having made that schoolboy error, you are now sitting back and watching them compete for a space that only comfortably accommodates one.
You did that. Not your wife, not your mother. You. Therefore you are the only person who can undo it; by kindly, gently, relegating your mother to a 'cherished peripheral' position, beside, not inside, your marriage.
The other thing implied by your 'rock and a hard place comment' is of course that you are the passive focus of others' attention and demands, not an active agent in your own life. If that is the case, you were not enough of an independent adult to commit to marriage in the first place.
This is a classic case of that phenomenon seen so often on MN from the wife's perspective; the man child who hasn't cut the apron strings and presents 'a DH problem, not a MIL problem'. That is, the wife perceives a problem with the MIL but the real problem is her DH, who has failed to develop an adult relationship with his mother and is incapable of asserting himself with her, in the interests of his wife, his marriage and his family (and ultimately himself as an individual too, as, in uncorrected cases, divorce looms, as the only way out of a three-person marriage, for the wife).