Wolf you better be emotionally centered if she does call the cops, and you better have that copy of that deed ready with your name on it. That is why most people here advised not to leave the house or the MBR. You have a moral obligation to protect your children you have a legal obligation to protect your home and your assets. Since you left for over a month or more she does not have any legal grounds to have the police throw you out of your own home however she does and can possibly have legal grounds to claim abandonment with your children in Family Court. You better make sure that any encounter or interaction you have with her within the household is recorded, and or documented. Depending on your state laws you may be able to record her without her having to know about it but might not be able to involve a third party as far as evidence and laws. Check with your local state laws first. If she files a restraining order, she could make up any reason Under the Sun for justification of it, and you will have to go through the trouble of having it vacated. If she becomes the first one to file the restraining order, what I want you to do is file a counter restraining order against her for you and your children and you better have the evidence and proof that she is having an affair and that is affecting your children within the home.
I've seen my brother go through this you better be prepared and fight for your kids with all you've got