My 1st grade CCD class is really wearing me down.
One thing that worked for me was to walk out with a child after class and talk to his/her parents right then. Explain the poor behavior, and ask for the parents' help in ensuring that it doesn't continue. I don't recommend that approach if you think the child has a disability -- just for those who are acting up. For the others, I would call the parents, explain the behavior, and see what they say.
Excuse me for sounding blunt but I'm confused why you feel you should shoulder all the burden with the disruptive kids in your class.
London Calling gave you some great advice.