If my husband abandons his family to live with his male lover could I deny visitation at his house and sleepovers. I have a 6yr old son and

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 supply

In 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

Until and unless the courts get involved, this is between you and your husband.  What might happen if this gets to court?  It depends on a lot of things.

Most family courts today refuse to discriminate very much, if at all, based on sexual orientation.  There has been too much experience with same-sex couples as parents, for the old stereotypes to carry much weight with most judges.  The focus is where it should be, on the best interests of the child.  If there is something about the partner's history or behavior that is or could be harmful to the children, that will always be fair game, and promiscuous behavior in front of the children is often frowned on, but gender should have little to do with it.

Truthfully, I would be more concerned about the financial irresponsibility than his lover's gender, on the facts you've given here.

And you haven't given all the facts here, quite rightly.  But you should, I think, get those facts in front of a qualified divorce lawyer in your area, very soon, so that you can get sound advice about what to do next.  One place you can look for an attorney is our website, http://attorneypages.com