Welcome to the american pants industry... specializing in baggy incorrectly marked clothing to make the american male feel better about his largeness. I started at 6'2" and about 245 and unless you want a hybrid for some reason you don't need to feel like you have to limit yourself.
It's also great that your kids are riding - you don't mention how old they are but once they hit 9 or 10 they can handle some pretty long rides so work them into your agenda. I get my 10 yr old out on a 20 mile ride as often as I can.
Last, you can't outride a bad diet. If you want to lose weight it will have to come from eating better foods (and probably less of it!)
Good luck and welcome to the forum!