Think it is outrageous that she thinks it is for her daughter's personal usage!
(I am assuming that it was a reasonable sized facility that you would expect to get several people and their babies in rather than say a single toilet cubicle
)
I would have gone to the nearest member of staff and asked them to come with me to tell the woman that she was not allowed to tell other customers that they weren't allowed in to the facility provided for everyone.
And in my ideal world I would have just been able to tell her not to be so ridiculous and marched into the changing room.
I was in the changing room / feeding room of our local shopping centre recently, in the feeding area, which is in a separate curtained off bit from the changing area, and has a sofa, chair, tv, couple of things on the wall for siblings to play with while the mum is feeding. There were 2 mums on the sofa plus a kid, one of them was feeding, the other had a kid in a pushchair and there was another little one roaming around. There were a couple of other mums that had to just stand and feed their baby or perch while feeding them in their pram because the non-feeding mum just sat and talked to her friend while ignoring the other kids.
To make matters worse, once the feeding mum had finished she scooped the kid from the sofa back into the pushchair and then changed the baby's nappy on the sofa without bothering to get up and use the changing stations that were all of 10-15 steps away. Didn't even bother to put anything down to protect the sofa in case of leaky poo 

Thought it was dreadful on all sorts of levels - selfish of people using the sofa to chat instead of letting mums that really could have done with it sit down, and just horrible and gross to stink out the feeding area when they could easily have moved to the changing station - and then to not even have bothered to put something underneath the baby whilst wiping up all the poo - ergh. 
sorry op, didn't mean that to turn into a bit of a rant about other selfish changing room users!