Jen, remember just because people say bad things about you it does not automatically make them true. Your ex husband is dealing with the issue that you left him for someone else, so he is going to be emotionally bruised and unreasonable. He wants you to be a bad person because then the reason you were unhappy is your fault alone.
You share custody of the children and have ample opportunities to show them what a good, supportive mother you can be. You have a chance to be a force for good in your childrens lives and make sure that they are aware of all the opportunites they have to have good happy lives and not make some of the mistakes you did. At the end of it all it is how the children view you that matters rather than your ex's opinion.
It is only a few months since you made this major change in your life and this is really a relatively short period of time. Things will be rough for a while but they will get better. People need time to vent. Also if your parents have been controlling before then there is no reason to suppose they will change now. Their behaviour is true to form. If calls deteriorate then don't stay on the telephone. Just say "I can appreciate that this is hard for you but I am sorry that I can't discuss things with you when you are this emotional , so I'm putting the phone down now. "
You don't have to be their whipping boy. There were probably more elegant ways to leave the organisation but the route you chose was swift and definite. It was always going to be messy but you need to focus on rebuilding a stable life for your children rather than the damage done. If you can move past it then after a while your ex will have to as well. Try to remain adult in all your conversations with him and as stated before don't let calls degenerate.
Best of luck.