I don't think it's abnormal - my closest friends would and have done this - they all know my daughter though and I know theirs, and their moms, sisters etc. (Because of exactly this I guess).
If it were friends I knew less well I'd find it odder.
If I realised DD would be with me when I had already accepted an invitation, and for whatever reason (time or distance or whatever) couldn't just leave her at home, I would phrase it more as
"So sorry, dd's dad has had to change access arrangements last minute, so now have dd. Would you prefer to reschedule, or shall I bring her along. Won't be offended and totally happy whichever you prefer. So sorry again. "
This has happened once or twice. Whether or not the person reschedules I think depends on what they are hoping to talk about at the meal/event, whether they want to seek advice on a personal issue etc.....
I think it's more understandable to ask to bring your kids than your mom, but I have at least a couple of friends who have asked to bring their moms to stuff a few times over the years.
My own mom would have no interest.....