If she knew your potty training policy before starting with you, than this is on her. Everyone has the right to do what they feel is best but I don't think parents should try to change the policies once signed on. If she doesn't want to follow your policy than let her go. She will most likely pull this "threat" move again when something occurs that she doesn't agree with and you don't deserve to have such a client.

I don't mind if a parent questions me, my approaches or policies. It's how we understand things, by asking for clarification. If they don't like it, we can have a discussion but I wouldn't be happy with a "change your ways or we're leaving" attitude. Most times we can come to a mutual decision or compromise and move forward