So freakmum has told her uninvited daughter that she could go with you and your family? That's not rude, that's insane!
If she has the audacity to say anything to you tomorrow, get the kids out of earshot and say to her firmly:
"There is a whole class party at the soft play next week to which, so far, you are still welcome to attend.
The trip tomorrow is a private family celebration, and I said that DD could invite 1 friend. She did.
You telling your daughter that she could come too and winding her up about it is out-and-out irresponsible and quite frankly CRUEL to your own daughter. You should be ashamed of yourself.
Think about what you do and say to your own poor children before berating me and mine."
Stupid COW (her, not you OP...)