Your situation sounds very confusing and as though you would be best served consulting with a divorce lawyer even if just to get some insight into your possible avenues at this point. Each state differs and as such they would best e able to serve you as well as if you explain the entire situation than an answer is easier to supplyIn short if you are still married they are his children as much as they are yours and to refuse visitation based on another individual being present may be hard to force. Most courts will not refuse visitation based on sexuality and again a local attorney will know more specifically.if you are not ready to file for a divorce without a court determination of who gets visutation, when where etc your husband has a right to see his children and his lovers presence would be up to him not you unless you both agree to certain terms