I, and plenty others here, can relate to being embarrased about our spouses/x-spouses behavior...especially in public.
It's like any brain cells that were left in that certain part of the brain were 'fried' or short-circuited when it came to proper behavior..or even self-control in certain circumstances. Not to care how your behavior might impact your kids, family is selfishness..plain and simple.
And the more you see/feel this, the easier it will be to distance yourself from the WAS...physically and emotionally. That doesn't mean that you don't still love them and worry about them, but it helps to know that THEY are the ones that are messing with their lives, and they really can place no blame on you or the marriage. They are living in their own little world that is so completely different than the world you had made together with your family/friends.
Yes, other people will comment about your WAS behavior...and that also will help you realize that it's all about them...not you, and not even really about the OP. It's what makes THEM feel good about themselves at the moment. They can't/won't remember the good feelings they had prior to all of this. The past has been re-written in their minds to allow for their present behavior, feelings and thoughts.
I'm sorry this affects your children so. Been there, done that...as many here can attest to also. Let the kids see you as the one that will not 'change' on them..give them something to believe in..something/someone to feel safe with. Security is so important to them through all of this.
Women are angels. And when someone breaks our wings, we simply continue to fly...on a broomstick. We are flexible