I agree.. remove the child's cell. Allow her to use your phone, any time she wants to contact the other parent. Before you give her your cell, block his/her number so s/he doesn't text her through your phone. You can always unblock him/her after each call.
Ask your lawyer if she can speak to the other parent via speaker phone so you can intervene when conversations become toxic. When it does become toxic and you're having to intervene, make sure you speak ONLY about the behaviour (in kid language) so she doesn't feel like the "piglet in the middle". Never defend yourself and always reassure her that you want her to maintain a healthy relationship with the other parent, as much as possible.
I'd stick to the schedule because this toxicity is likely happening during visitations.