You're with a jealous controlling bully.
This is something you've chosen to continue with, and something you've chosen to be witnessed and experienced by your child. You can unchoose it.
Attempting to control who a partner can and can't see is worrying isolating behaviour - 'why do you need anyone else? You're with me now' is a well known tactic. And the fact it's another woman doing this to you about your own mother is irrelevant.
And her claimed reasons are nonsense.
I wonder if she has issues and insecurities with the fact that you're the baby's birth mother and she isn't?
Or that you being close to another woman, your own mum, is somehow a threat to the relationship?
Totally speculating here but what lies beneath this? Some sadness in her own life and childhood?
You need a full conversation about this. Find out exactly what the problems are around this.
Set out to yourself what you want to happen and why. Tell yourself
My partners behaviour IS strange, unreasonable and controlling.
She tries to emotionally manipulate me.
I need her to stop behaving like this.
And practice your statement to her.
I have a right to see anyone I choose, especially my own mother.
I need my mother's support and closeness.
My baby will need and love to have a relationship with granny.
I am taking the baby to see mum on mother's day.
Then when you tell her, stay in control of your own behaviour, language and how you speak (you've said you sometimes get upset and say things you regret).
Watch her behaviour and reactions, as if you're a scientist observing.
Ask yourself is this the response of a completely well and rational person?
Do you want this for yourself, your mum and most importantly your baby?