How sad about your mum’s reaction. She sounds high maintenance which is not what you need.
You can initiate contact without an apology, just carry on as normal and that might help take away any awkwardness.
Could you message her to ask if she’s still ok to take you to the hospital on Saturday and if not, you’ll find another option?
If you can fake that everything is normal it might get back to normal more quickly and she’ll have had time to come to terms with her disappointment.
You’re not unreasonable to be changing your mind and wanting it just be you and your dp at the birth. She’s not unreasonable for being disappointed that she won’t be there as she had thought she would be but she is being unreasonable making you feel lousy and unsupported.
Ironically she might be pushing you to lean more on your MIL if she continues to be so emotional and challenging of your choices.
I’m very close to my mum but she wasn’t at the birth of our children. She might have been at the hospital for part of the labour but I don’t really remember. My abiding memory is just of me, my husband and the dr. Both births were the most profound moments of my life. Looking back it was absolutely right that it was just me and my husband there.
It should be your mum’s responsibility to show you all is well but life’s too short, in your shoes I would want to get things back on track ASAP and focus on a calm birth.
If you carry on as normal, she will see that you mean what you say and aren’t letting it become a big issue.
Her reaction in many ways validates your decision. She doesn’t seem very dependable.
But don’t let what’s happened detract from the amazing moments to come, all the best with the birth and hope you can resolve this issue with your mum quickly and not let it fester.