Hi network. I think it helps if the other parents in your group have similar family set-up and needs to you, and not just ages of children. I have never organised a formal support group, as such, but tend to find the friends who help me the most are the ones who are most like me. But it takes lots of looking to find them!
For instance, some of my son's friend's families had lots of backup already, via extended family, neighbours, old friends living nearby, so simply don't have the need to offer support and expect support from me. (I don't have any family I can call on or likeminded neighbours, except in emergencies).
Also, of course, there is an element of risk in getting relatively unknown adults to look after each other's children. It is not as if they are registered childminders, or their homes are insured for childcare. And if a well meaning adult offered to pick up my children from school every day, I'd be extremely grateful but also need to know how reliable they are. If people feel they are simply doing favours for each other, they may feel more free to cancel arrangements.
I also think people have to be very sure of each other and their parenting styles before agreeing to swap duties, and of course it can take time to build up that trust and knowledge. Perhaps if you start building up some sort of social support network (get people and their children together for park dates, ets) with a view to helping each other out, then once everyone is at ease with each lother, start to sort out the child care angle?
I think it's a great plan and good luck with it. I wish I or someone I know had been determined enough to start a local group like yours around here.