Former drag king here!!
I say go for it! Drag is very liberating.

I founded and was part of a troupe called the Mambo Drag Kings here in Montreal about 10 years ago. I do some emceeing for community events, and the idea came to me that I wanted a possee of drag kings dancing behind my first lipsynch number (not in drag). Eventually, I just started doing drag because the troupe kept being asked to perform and there wasn't much interest in just having a woman lipsyncing (how do you spell that??). We did shows at clubs and community events for years. It was a blast. We're not officially dissolved, but most of us are too busy now to keep it up. Two are real die hards and still going at it!
We did mostly retro stuff, and our style was elegant and classy. We wore suites for the most part, if only because they are best for hiding the female form. We did Tom Jones a few times (It's Not Unusual and Leave Your Hat on, which we performed at Pride in front of 10,000 people. Yikes!), and classic songs like Love is in the Air. We did Prince one but it was a disaster!
In recent years we got into more gender-bendy stuff. We did a number from Cabaret (Mein Herr) where the kings were all dressed in white shirts and black pants but had make-up on a-la Joel Grey (I was the girl lead in that one), and we also did Wilcommen, with me in Joel Grey drag and the "guys" in colourful boxer shorts, sock garters, shirts and ties.
Binding: ace bandage, for sure. But the real deal for us was the facial hair. It took years for us to master that. We used fake hair that we cut up really finely and eyelash glue. For a while we had an actual guy come and do the hair for us, which taught us lots.
My stage name was Phil Lerrup (say it fast; get it? LOL!)
Drag also brought me my family: my partner and I met when she joined the troupe. We fell for each other when we were filming a mock episode of Dick Van Dyck called Dyke Van Dick where she played Dyke and I was Mary Tylor Moore. Major sparks.

Hilarious! The movie is called Kings, and it has shown at some queer film festivals.
As to what your kids will think, that depends on them and how you present it to them. Good luck with that!!! Haha!