Ironflower -- This is beautiful:
What You said -- "Okay, lets move forward and forget it. We just want to know if we see you that we won't get the silent treatment, eye rolling or pushing the boys away from you"
Mum - "Not promising that, you hurt us and we are angry".
Because your Mum was 'hurt' and even though You were willing to let it go, your 'mom' still had to resort to, and this is my Abuser to English translation -- "I'm always angry which is why I lash out and hurt people. You just told me what in my behavior is unacceptable, the eye rolling or pushing the boys away from Me BUT because being angry is my 'normal self' of course I can't promise I won't repeat the behavior because that is My (dysfunctional) 'normal'."
When a 'parent' talks like that? Believe them and then go No Contact.
Instead of owning/accepting that she IS an 'angry person'/abuser my 'mom' like yours justified and self-excused her own behavior by declaring that she was only 'angry' because the people around her "made her that way".
Abusers/dysfunctional thinkers are ANGRY as their 'normal'. They believe it is up to everyone else around them to make sure their wrath doesn't 'erupt'. That is a LIE. There is no amount of anything that will 'fix' their anger no matter how much those around 'them' try.