dx ... I am not one of the pros around here, but I think all of them would advise you seek out legal counsel. If you disapprove of the children being around the OW (and it sounds as though you do), a lawyer may be able to help you draft the appropriate paperwork to prevent that from happening.
Please remember that right now your h is focused only on what makes him happy and is not focused on what is in the best interest of the children. Unfortunately, you are going to have to find a way to carry that burden alone.
I will let the pros chime in from here.
2t2m
Me: 59 and holding H: :53 Me: 1 S, 1 D, both grown M: 19 T: 23 BD: 9-23-2013