Yeah this is fucked up, don't mind her mood-swings whenever you put your foot down, take the 'as far as I'm concerned it's over'-stance. If she truly, direly wants you back, she'll eventually come running to you, and if she does, don't just take her back with open arms. Be like making sure it's not just a desperate attempt to exhort a final display of your emotional attention.
And overall don't be nor seem desperate to be friends, don't go out of your way to hang with her. Be casual.
Sincerely just move on.