In terms of the upset,
it’s about feeling like she doesn’t value me I would ignore it. Why are you worried about how she values you when you have a good (on the whole) relationship with her and your husband has chosen you as his forever love?
She maybe feels in competition on Mother's day - I know one of my daughters always wants to visit me on mother's day but actually it's more important (to me) that her boys get to "treat" her especially well on that day and she experiencs the days they wake her too early with cold tea and biscuits in bed (!) and will remember the warmth of her love as they grow up.
My gift to my daughter is releasing her from coming over to me. Maybe your mother-in-law can't release your son so easily and wants him to visit/take her out or similar - in her role as matriarch?
I have no idea why she forgets your birthday. Probably because she didn't have the date engraved in her heart when you were born - as she did for your husband and your children (who are obviously special as they are her only child's children!!).
If it helps, I have to check some of my grandchildren's birthdays - and two of my son-in-law's, and both my daughter-in-laws birthdays.
I may know they are, say in the spring, mid February, over the Summer, in November etc but I have to keep looking them up in old WhatsApp messages.
I do not miss them out - as I want to get it right but it's not easy. My "birthday book" has been mislaid some time ago and never replaced.
I think it's less personal than you think.
I truly love my daughters-in-law and sons-in-law because they love my own adult children and this alone is a precious gift to me.
I will not be here forever and I want them to have someone else who loves them to walk with them through life.
YOU are the special person in your children's life - and to your husband. That is validation enough. Bask in their love and let your mother-in-law do her own thing.

I do think your husband should question why she gets him father's day cards though! 