Ywbu totally! Not just leaving her (a very young baby!) with a child, but one with I'm guessing reduced mobility due to the ankle too?!
I'd have waited until baby woke and then taken her to shop with me.
In dd1's position I'd feel I could never trust you while baby is still so little. It'd take a long time to rebuild trust.
Making that decision for your own child is one thing (and still not one I'd make) but when it's not even your baby? No.
And I say that as an mner who's generally quite relaxed about age of babysitters having been one from 14 myself but 11 is FAR too young if anything had gone wrong.
I've since spent over 30 years looking after other people's children inc babies & I really wouldn't have done this with such a young baby. Their health/safety can turn on a pin! And they need someone there who can react appropriately if so.
Also in my experience people massively underestimate how long a thing takes to do. My mum will say "X is 5 mins away" when it's actually 15-20, I've known people say "doing X only takes 5 mins" but honestly? Have you ever actually timed how long to walk to corner shop, find item, queue (unpredictable), pay for item & walk home? I'm betting it was longer than 5 mins, closer to 15-20 mins in which time a lot can happen.
Ultimately your dd trusted you with her precious very young baby and you betrayed that trust, and you're one of only 2 people she really feels she can rely on right now.
"DD2 can't walk from the living room to the kitchen at this point." That makes it worse not better! She clearly can't move fast enough to deal with if baby had vomited and needed mouth/nasal area cleared, started having breathing difficulties or a fire broke out. All possible scenarios.
"She has spoken to her GP about it and she may have PND." All the more reason NOT to add to her stress, even if she'd not come back when she did dd2 could have let slip, or you could have told her thinking it was fine. Actually that also makes me think you were longer than 5 mins or else you'd have been on your way back and seen her arriving, going in the house, talking to dd2...
Contrary to several on this thread I didn't leave dd completely alone at that age if I went to loo or had shower. I generally tried to bathe/shower when her dad was home but if there was a poonami or vomit explosion & I needed to she was in Moses in bathroom with me, ditto if I needed loo (big bathroom at that time).
"she should have brought nappies but let the mum who remembers everything all the time cast the first stone." Definitely.
ALL that said she shouldn't have said what she did BUT she clearly got a fright, is not well & is feeling really stressed so that will be why. If you apologise in all likelihood you'll get one in return (and probably her telling you all that's worrying her) and you can sort out between you how to move forward.
But I still wouldn't have made the same decision you did.
Op can certainly promise not to do it again without checking with dd1 first.
"you did the only thing that you could do" no there were a number of other, sensible options.
1 wait till baby wakes and take them with you. As the shop is so close by it's not going to mean baby in dirty nappy too long and a little fresh air does no harm if baby has a slight cold, wrapped up warm will be fine. Could even have called dd1 to discuss this being necessary due to lack of nappies.
2 called dd1 to bring nappies
3 used any number of household textiles as nappy sub, babies managed for 100's of years in cloth nappies and still use them today
4 asked a neighbour or friend to bring nappies
"What is this thread was
Hi, my mother was baby sitting my 8 week old baby whilst I went out with some friends.
I returned home early to baby chocking on some spit up, with my 11 year old sister who was unable to get her to die to a bad ankle that she can’t weight bare on.
My mum had gone to the shop and left them un attended.... would we all be saying the same ?" Exactly, think we'd be seeing very different responses.