My exh and I co-parent and seem to manage it fairly well. The children are 12 and 8 and spend 2-3 days with their dad each week. We live 5 mins away and we make a big effort to 'get on' for their sakes.
We consult each other if either of us notice any issues regarding the dcs, eg. dd had a few problems at school with her friends. We go to parents eves together and have been to a couple of concerts together - we meet at school, go in and sit together and then leave separately.
I make most decisions regarding school trips, activities etc and I pay for clothes, school dinners etc as they live mainly with me but we I consult him on major things like dd getting braces on her teeth.
It's not easy, and if it wasn't for the children I would prefer to have cut all ties with him, but we decided when we split that we had to do it this way because we'll be parents for the rest of our lives. We decided that if possible we would always keep a united front for anything that involved them.
We both have new partners, and mine is completely understanding which really helps (not sure about his yet) Neither of us live with them yet though so not sure how the dynamics will change when that happens.
Most of all we both seem to agree that the children's wellbeing is very important and we consult each other if either one of them seem upset for any reason, so we know what each other has said to them.
If anything it has meant that exh is much closer to the dcs than he ever was when we lived together. He is much more involved in their lives whereas before he wasn't interested and left everything to me. My dd (12) in particular says she really appreciates that we get on ok and theres no awkwardness between us.