Oh dear, @Emthebaker - there is so much more going on besides the main point of your post, isnt there?
I’ve tried to explain this to my mum and asked her to respect my decision, but she has told me it’s not my place to dictate to her and said if my decision is final then ‘we are done’ and she has not spoken to me since.
Not your place, to decide for your own baby?!
Your mum is prepared to not speak to you over such a minor issue?
She is a controlling, manipulative, selfish piece of work ...
However -
Is it worth all this aggro just over what name your baby is going to end up calling DM's DP?
It's complicated with blended families. My GD has 3 grandmothers. She (ie my daughter decided for her) calls us 'Grandma Anne, Grandma Betty, Grandma Carol'.
That way, nobody gets precedence, & nobody gets confused.
Of course you are going to want to honour your dad's involvement in your baby's life by calling him Grandad. I suspect your mum's insistence that HER DP gets the title is far more to do with rivalry & showing her ex-DH who's boss.
But could you compromise by calling mum's DP eg "Grandad Joe"?
I'm not recommending that you lie down & let your mum walk all over you (which, reading between the lines, sounds like par for the course from her). But I am suggesting that you might not want to choose THIS particular hill to die on. There will be battles aplenty to choose from as your overbearing mother adjusts to the fact that YOU are the mother now, & attempts to take over in various ways. I'd really save your thunder for then.
Conversely, you could decide that this is your line in the sand, she doesn't get to dictate to you, or make her DP who makes little effort with you "Grandad" ahead of your own dear dad.
The trouble is, at some point she is going to pull her emotional blackmail stunt again & threaten to not speak to you unless she gets her own way, so - I am so upset as I obviously want her to be a part of my little boy’s life. - I think THIS is where you should be focused, not some daft row over who gets to be called what by a baby who isn't even here yet.
You may find yourself in the not-too distant future needing to call her bluff, or be controlled by her forever. Your finance has obviously go tthe measure of your mum: To make matters worse, my fiancé doesn’t understand why I am so upset and feels I should have seen this coming due to my mum’s previous pattern of behaviour.
& I think you should absolutely prioritise a long talk - many long talks! - about this with him.
It's easier to spot the pattern from the outside, & the one on the inside can be drowned in a wave of FOG (fear, obligation, guilt - google it!) & unable to navigate away from the FOG-creating relative.
Try thanking your fiance for his insight, & asking him how he would have tackled it differently. It's no use him saying "I told you so" - he needs to get on board & support you 100% in presenting a united front to your emotionally blackmailing mother.