I personally feel like you should share it with mum and MIL, and then have your own Mother’s Day from you intermediate family.
Are you able to do what you want as well as pop in and see one or both? Doesn’t even need to be that day. I used to take my mum out for afternoon tea on the Saturday. I might pop in and see her Mother’s Day if we had time. Mil only had one Mother’s Day with us and I think we invited her to the farm.
We typically do a family gathering the week before or after Mother’s Day and then spend the actual day by ourselves
We usually spend the day with my mum, and my partner will go see his mum at some point
I used to share with my MIL. my mum lives 100+ miles away so it’s not always easy to get together but since my MIL passed i normally just do something with my husband and kids
The whole weekend for me is Mothers Day. I’ll have a brunch day w my sisters and My mum. Then hubby will take me out for dinner seperately. Then that weekend or even the weekend before/after we have a girls night and celebrate us no kids no men. So I have the Thursday, Friday, Sat and Sun as Mothers Day
I am yet to get there, but personally I believe that the priority is you now as the new mum. Your own mum and MIL should be supportive of this day being about you. If you’d like tos show respect and love to them, you can always get them a card and some nice flowers. If they have an issue, just take a breath and put a boundary. You and baby are the priority now. Your partner shouldn’t even think about celebrating Mother’s Day with anyone but you. Celebrate you mumma! ♥️