There are TONS of volunteer opportunities in the summer that would be happy to have you! Branch out beyond the schools. In fact, many schools really don't want the parents of their students in the classroom - it's a huge distraction and creates a problem with confidentiality. There are many many places that need you more than a classroom needs a party. Try to see that ANYTHING you do in the community benefits your children because you make the world a better place, and they see you doing it. That's how they learn to give and not just receive.
Most towns have summer recreation programs. Many day camps would like to have someone help out - possibly in exchange for camping slots for the kids.
Food pantries are absolutely desperate in the summer. Schools and companies are on "vacation schedules" but more and more kids are hungry because the school lunch and breakfast programs aren't operating. They need people to help organize food drives and raise awareness - in neighborhoods, in companies, at supermarkets, etc. This is a good program to get kids involved too - helping to stock shelves and learn about hunger.
Red Cross blood supplies drop to critically low levels in the summer because companies slow down with blood drives (and employees/donors are on vacation) and colleges are not in session. They welcome volunteers for blood drives and donor centers.
There are plenty of neighborhood kids available to help with babysitting in the summer, so you can have more time available than you think.
I think, if you branch out more, you'll make many more contacts than if you confine yourself to the schools.