I thought you had it legally set up where your wife can’t just barge in like that.
What your wife did was intentional and all transactional. She WANTS to upset you. So she got some guy with money. Not surprising because she is a user and has this guy convinced she is a victim. Users don’t love or respect. This guy will eventually see this about her.
Tell your lawyer what happened. Remember, people who act this way are insecure and selfish. Don’t react because this is what your wife wants. I’m sorry you are so badly triggered, everyone posting to you can tell your wife is selfish and abusive. And she is probably still abusing alcohol.
I don’t think she is allowed to just show up and demand an audience with your daughter like that. After all you do have full custody. Please talk to your attorney.
Remember, narcissists cheat and lie and like to create illusions.