1. Who is or is not invited to a shower is entirely at the discretion of the shower's host or hosts. If I'm hosting a shower for my great niece, then it may be that my guest list is made up of my own little old lady friends. I'm not under any obligation to include anyone from the groom's side, not under any obligation to include Mamas or bridesmaids or anyone else I don't choose to invite. My great niece (the bride) might decline to come meet and accept a shower of gifts from my little old lady social circle, but my great niece doesn't presume to tell me who to invite or not invite to eat, drink, and make merry at MY expense. That goes double for the groom's Mama.
2. An invitation is an OFFER, not a demand. An invitation says "If you'd like to enjoy refreshments and fun in exchange for bringing a gift, you're very welcome to join us." A host who can't take "Thank you, but I can't be there" for an answer is a host with a very inflated sense of entitlement.
3. If this story is complete and that's all there is to it, then the groom's Mama has some unusual ideas about how parties work, about the HOSTS being in control of their own parties. If she's mad then she either gets over it or dies mad.