Not really sure I understand the question. Are you asking if there's a way to completely and absolutely prevent her from calling the police? I hope you understand that would be absurd. If that's not what you're asking, you'll have to clarify.
Taking the second part of this question first, the law has nothing to say about the living arrangements of married persons and their children. Unless one of you seeks and obtains a restraining order or files for divorce, there are no legal restrictions on either of you taking your child anywhere at any time (save for the fact that passports are required for international travel).
As for the first part of this questions, the only way for either of you to compel the other to leave your marital home is to seek and obtain a restraining order or file for divorce and obtain an order for exclusive possession of the marital residence.
Since you seem to be heading for divorce, I suggest you consult with a local divorce attorney.
As phrased this isn't a question, but it appears New Jersey does not allow parties to seek a legal separation as an alternative to divorce.

