Yes, it is legal--the law does not regulate morality or the domestic relations or arrangements of adults, even married adults, in that way. Whether spouse brings partners home is between the three of you, so to speak. The one exception would be if the circumstances or the partner in some way poses a threat to the children; in that case, you may be able to call child protective services to have them intervene, but it would have to be a real *threat,* not merely exposure to a situation you'd prefer they remain unaware of.It is certainly possible that this will help your case for custody, since even if not illegal, it may be evidennce of a cavalier disregard for the children's interests and feelings. You should discuss with your matrimonial or divorce attorney. (If you don't have one, get one--the attorney will drastically improve the odds of getting the best outcome possible.)