First, being connected to iCloud Photos when it's full is asking for trouble. Things that you do on the phone are trying to talk to iCloud and not getting a proper response. Many ordinary operations will become glitchy. The same is true, by the way, if the iPhone's storage gets to be more than 90% full.
To fix the face mixup, you need to go to every picture of Mom or Daughter, open the info window, and click on "This is not …" Do this even for the ones that are correct! Photos has learned the characteristics of both together, so you have to erase all its memory of these people. Then, you name them Mother and Sister (or whatever, but different from the original names.) Then Photos can learn the characteristics of these two "new" people, and it won't get them mixed up. You can go back later and change Mother to Mom if you like, but I'd give it a while to completely forget the old features.
But you should fix the storage thing first.