To be honest I cannot think of any logical reason why the BM would think that withholding parenting to be an effective punishment for your child misbehaving. Does she view your parenting time to be nothing more than good times and fun and games?
Maybe you should follow her rules and the next time your child misbehaves during your parenting time refuse to return the child to her as a form of punishment. Seriously, you need to convince her that you do parent your child during your parenting time. This includes giving guidance, discipline, boundries, structure, chores/responsibilities, etc. In short that you are acting as a parent and not just a good time buddy.
Maybe you should follow her rules and the next time your child misbehaves during your parenting time refuse to return the child to her as a form of punishment. Seriously, you need to convince her that you do parent your child during your parenting time. This includes giving guidance, discipline, boundries, structure, chores/responsibilities, etc. In short that you are acting as a parent and not just a good time buddy.