OP,
She's a nasty bully.
And your partner is no better.
You say you are a wimp.
Is it because you have surrounded yourself by bullys?
Is that what you want for your daughter?
To grow up watching her mothet being bullied and her father standing by.
What an awful environment for a child.
I really don't understand how anyone accepts this.
You are accepting it from your FIL and MIL.
I cannot stress how unhealthy this environment is for a child.
You need to think long and hard about your decision to have a baby with this man.
Because it sounds as if the fact that he is an only child his mother can behave in any way she pleases, to the clear detriment of your daughter.
So your MIL is more important than your daughter?
Your MIL's need to bully and belittle you comes ahead of your daughters best interests?
As others have suggested.
Spell it out to your partner ONE LAST TIME TO SORT OUT.
If she says a word pick up your child and leave.
Ask her to leave your home.
This is deal breaker stuff.
If you care about your daughter, you will be prepared to tell your partner you will leave him BECAUSE of his mothers behaviour.
Take this seriously NOW and nip it firmly in the bud.
What sort of family do you have, that you would accept this behaviour in your home?
Dramatically reduce the time you and your child are in her company.
She has NO entitlement to see your child if she uses that time to bully and belittle you.
Good luck.