Hi, spiralinggup, and welcome! Alas, I don't think you'll be able to patch things up. I do think children watch how other parents respond to things and then try them out on their own parents. It sounds like the daughter knows she'll get a response when she lies about your children.

Ignoring is okay, in my opinion, for little things. You don't want to reinforce those behaviors. But people are smarter than the animals Skinner studied.

My two cents' worth anyway. Interesting and important issue. I'm glad you brought it up. What do other parents here think?