Is the 20-year-old still at home? For him/her, I agree with the explaining that somebody else mentioned--your reasoned decision as to why you're leaving.
For the 16-year-old... maybe. Let me tell you how it's gone with my 3 girls, now ages 17, 15 (almost 16) and 13 (almost 14).
We were uber-spiritual... one of the 'cornerstones' of the congregation if you ask anybody. My girls were popular, but with the 'faithful', not with the 'in' crowd of kids. You said your kids are popular--if it's with the 'in' crowd, the 'popular' kids, you're probably not going to have any problem pulling them away from a WTS routine of life.
With my girls, I'm lucky that my wife (who is still a JW) and my kids stopped attending meetings regularly. They say the reason they stopped was so as not to unduly add to my stress, as they know that JW stuff really 'gets' to me. I think, based on things my wife has said, attitudes she's voiced, that she doesn't 'buy' everything JW's teach, or at least how the organization is ran. She's voiced the words 'the good-ole-boys-club' before.
Now, with the kids not attending meetings regularly, my wife has been very open about letting the kids do things we didn't let them do before... they hang out regularly with both witness friends and friends from school, sometimes at the same time (when it's at our house). They go to their school friends' homes, go meet them for lunch or movies or other activities. My oldest is participating on an OVERNIGHT away trip this weekend in the Academic Decathalon, traveling and staying with non-JW kids and chaperones, without my wife or I along, something we would never have permitted when we were 'in'.
And you know what? Our kids are HAPPY, they are having FUN, they LOVE their new life, and they DON'T MISS THE MEETINGS.
Just let your kids be kids... let them live a "normal" life, be an active and concerned parent, but not a domineering controlling JW one.
You won't have to "prove" your stand to them. They'll see how much better it is, all on their own.
Just my 2 cents worth.... I wish you the best!!!