It appears you have questions about a separation in addition to questions about real property. It's difficult to give a definitive answer in to your question because it will probably require some document review.
I have a real estate practice in the area, and I'm happy to sit down and discuss your questions in a confidential setting.
This communication is intended only to provide general information. No attorney-client relationship is created.
If yiu are married and deed is in both names, then you can live in the same house unless there is an order granting your wife exclusive possession. Consult with a local divorce lawyer to help you.
If this answer is helpful, then please mark the helpful button. If this is the best answer, then please indicate it. Thanks. For further information you should see an attorney and discuss the matter completely. If you are in the New York City area, then you can reach me during normal business hours at 718 329 9500 or www.mynewyorkcitylawyer.com.
You are right. You are not "legally" separated (you may not even taken the first proper steps to a legal separation) you are not under a court order to cede possession of the house to your spouse, there is no order of protection barring you from the house or mandating you keep a distance from your spouse, you own the house and are responsible for the mortgage, is there a reason you believed that you should not be in the house.
A married couple contemplating dissolution of a marriage are well-served by early consultations with marriage counselors and attorneys. Your home ownership, child-rearing and finances are entwined. As long as you are living together, you are not "separated."
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.