His desire to dress this way has little, or more likely NOTHING, to do with you.
A great idea might be to ask him (gently, inquisitively, sincerely - so as not to create conflict ) "Most crossdressers had the desire to wear women's clothing from a very early age ... when did it start for you?" And then LISTEN.
Another great idea ( to get you some true insight into the future ) is to ask: "Would you like to plan a short vacation to another city where nobody knows you and get one of those consultants who help men do a complete makeover with clothing, makeup and wigs that "pass" and accompany you in a public outing where you can feel safe?" And then LISTEN... and a day or so later, discuss some ground rules for his indulging at home.
Regarding your kids, unless you're in a very small town, they've been indoctrinated (brainwashed) by the school system and media to think this is not only "acceptable" behavior, but "desirable" behavior, so I wouldn't worry TOO much about that.
Stats show that MOST crossdressers are heterosexual ( interested in opposite sex ) and the fantasy for us has many motives.
Some just like the texture and feel of women's clothes. Others do it just to de-stress and not "be a man" and hold every emotion inside, so, perhaps it might open lines of communication about his life's worries which he deals with ... IF you are cool about it.