A co-parenting arrangement is sometimes a good idea for the children, but it can be rather difficult for the parents. When you are going through this situation, you need to be prepared for handling conflicts with your ex. This can be a challenge but with respect and proper planning, it is possible.
One of the first things that you have to remember is that you don't need to judge your ex. There is a difference between discernment and judgment. No adult wants to have someone else always nitpicking what they are doing. Co-parenting isn't any different.
When you don't agree with something your ex is doing, the first thing you have to figure out is whether your children are in danger or not. If they are in danger, it is time to stand up to your ex. If they aren't in danger, think about how the situation is impacting them. If they are healthy and happy, you might not need to do anything.
Remember that conflicts have to be handled on a case-by-case basis. You can't try to lump matters together when you are dealing with co-parenting disagreements. For example, don't try to say that you aren't going to allow your ex to come to the holiday gathering that is customary if they don't agree to allow your child to go on a field trip they don't agree with.
Serious conflicts might mean that you need to turn to a professional to help resolve the matter. Ultimately, the goal is to help the child live the best life possible. Every decision you make must reflect that point.