Youa re so set on having a friendship with someone who doesn't want to have a friendship with you. Her definition of "friendship" is getting you to do what she wants. Otherwise she has no interest.
A friendship sure, would be ideal, if that was in the cards right now and she was in a healthy place to do that, but it is more detrimental to the situation. You trying to form this "friendship" is no different than trying to reconcile with her now.
Throw the friendship out for now. Keep contact to the minimum, do the right thing for your boys that is within you reach.