It does sound like your mother is massively over-involved op.
Do you think she is thinking ahead to when your ex’s baby is born? Maybe she is worried on your behalf about finances ? And also how your ex will split his time? Or that he will be a less involved father to your child overall? Or somehow that your grandchild will be less “special” and slightly on the outside of your ex’s nuclear family?
Or, in the year that your mum facilitated contact, she might have thought that to an extent that she was in control, that she had somehow made it all run smoothly and your ex was developing a great bond with his child because of her and she enjoyed being at the centre of it all?
And now your ex has a new relationship, she might feel jealous of the “new” woman on the scene who will be your child’s step-mother? (Not jealous in a wierd way but she’s worried that she will become third in the queue after you, and the child’s step-mum? That she has been replaced somehow?)
Also, during that year, your mum probably poured a lot of love and energy in to your child, and in to facilitating contract, and now she is not doing that any more, she doesn’t have anywhere for those feelings to go? She feels a bit redundant. And maybe can’t move on until she’s had some formal acknowledgement from you of what a great job she did?
The way to solve this is to do what you are already doing, but more, that is, take charge. Don’t rely on your mum as much or talk to her about your relationship with your ex. Emphasise that this is a new phase and you and your ex are moving on and that she should do the same?
Maybe invite your mum out for a special lunch and give her flowers and a card saying how how grateful you were for all
of her help facilitating contact and that you couldn’t have done without her support (reminds her of her importance while drawing a line under past).
At the same time tell her gently but firmly that she needs to stop obsessing about your ex’s life and focus on her own (demonstrate how you are moving on with your life too so she has no need to worry.)
Emphasise that it’s a new chapter now and ask her what is she doing with all the extra time she has? (Redirect her focus.).
Finally, suggest some fun things that you, your mum, and her grandchild might like to do together in future? (Reminds her that she’s not redundant and there are new things to look forward to.)
If none of that works, and she won’t or can’t leave it alone, go grey rock and slightly step back from her and every time she mentions your ex say something like “leave it alone mum please, we’ve moved on, why haven’t you?”