I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
There are a couple of options here. First, anything that you and your wife agree and put in a written settlement agreement will be upheld, but she might not be willing to agree to that. Second, you can request what's called a morality clause, stating that neither parent can have an unrelated overnight guest while the children are in that person's possession. That would prevent her from having her boyfriend sleepover, and that's pretty commonly granted when requested.
If you do not want your daughter to have ANY contact with your daughter, period, then you have to show how he presents a danger to her health and safety and how it is in her best interests to have no relationship with him whatsoever. Things that could help in that regard are if he had a history of drug or alcohol abuse, child abuse, a violent criminal history, or something like that. If you or your daughter have witnessed any behavior that suggests he shouldn't be allowed to be around her, you can testify as to what happened. The judge typically won't enter a full restraining order on a parent's new dating partner without a very good legal reason. The fact that the mother had an affair, in and of itself, isn't enough. But if there are other reasons your daughter is better off without knowing this man, yes, you can make the request.
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