Real Estate Deed Co-Owners in DE?

I am a divorced woman. I live in the home with our 6 children. Their father & my ex-husband does not live with us. We did not do an asset division, or any other kind of agreement, in the mutually agreed upon, non-lawyer divorce. My boyfriend of nearly two years will be moving in on Friday. He is concerned because someone (not associated with the law in any way) told him since my ex-husband is listed on the deed of the home first, my ex-husband has "extra" rights and could call the police and have my boyfriend legally removed. Is there any truth to the "listed first=extra rights over me"? I asked each of my children if this move-in was okay with them, and they all said, "Yes.". I asked my ex-husband if he is okay with the move two weeks ago, but I keep being told, "I am thinking about it." when asking him for a definitive answer since then.