No I'm not controlling at all, my mum is though and she fucking loves that she met DD first.
...and there is the real issue.💐
DD is yours that is ALL that matters, you & her are here & well. Hang onto that.
Definitely don't ask them to delete the photos, don't lower yourself to their level & don't show it bothers you.
What you do though, depends on your personality & theirs. You have options. Go no contact (not because of the photos per se, but because a mother who 'fucking loves having met her first' is clearly someone who causes you upset). Ask her to exchange the photos for others and that tell her that if she doesn't, you'll understand, but that you will not visit. Take every single opportunity to remind her that she might have seen DD first, but she's yours and you get to see her every minute of every day whilst your mother gets to see her when you allow it.
Take control for sure, but don't get the photos deleted, you might regret that (not that I think they'd do it anyway).
If you haven't so ready, check out the Stately Home threads.
A thought for you, for future posts. Your mother is nasty, the dynamic is terrible. Be careful to put that out there, up front, or else you will be told you are nasty/controlling/selfish whatever, because posters assume your mother is a loving, caring, nice, person - if not warned otherwise. I'd hate you to feel her treatment of you is 'OK' because everyone here thinks do...when in reality they don't have the full picture.