I have raised one stepdaughter, who is now 26, and now am a newly-single mom with 3 boys, 13, 10, and 3. I would, if I were you, NEVER ask your stepkids to babysit your 6 yr. old. It is not their responsibility; it is your and your so's.
In the 6 years that I lived with my stepdaughter as a teen (13-18; then she left for college) I never asked her to watch her half brothers, who were babies and toddlers at the time--and whom she loved very much. But she was a teenager. Period. Teenagers do not want family time with a little kid, and there is no reason whatsoever that they should. I've read many, many books on stepparenting, and the one rule that has come up again and again is this: don't make the mistake of trying to make your new family into ONE big happy family. Respect your differences! You are the parent; and even teens need support and family; but mostly they need good role models, space, some guidance, and some very carefully selected responsibility. Ask them what *they* would feel most comfortable doing to help out the family. Is it doing the dishes after dinner? Would they rather help make a salad before dinner? Or just do their own laundry? Anything that gives them some responsibility, but does not make them resentful.
Taking care of a 6 year old is something that I personally, at 44, would never, ever volunteer for. Some people, and some teens, would love it. But obviously not these teens! So try something else. And yes, pay them if they watch your son. And don't worry!! Forcing unwilling teens to spend "family time" together is only going to make the problem worse. They may come around in time, but ages 15 and 16? I don't think so.
By the way, my now soon-to-be-ex stepdaughter absolutely adores her brothers and loves spending time with them now. She visits them every few weekends, takes them to movies, shows them funny restaurants she's discovered.....It's totally different now that she's an adult. Don't lose hope for a "whole" family. You just might have to wait longer than you expected. And your family IS whole, already.
I wish you luck! I really needed it in those years of blended parenting. It is so, so hard.