Having to work with your ex on child custody matters isn't easy for most people. When you have to deal with one who is passive-aggressive, you might find that life is a lot more difficult than when you can get along together. There are many things that you might be able to do to make it a little easier to deal with your ex.
One thing to remember is that people who behave in this manner often claim that they can't do something when the truth is that they just don't want to do it. You need to figure out how to deal with this when your ex is trying to play on this point.
Another thing that might help is to remain flexible. Nothing is going to go exactly as planned all the time so if you are able to look past the minor inconveniences, you might realize that the situation isn't as bad as what it could be.
There might be times when your co-parent gives you the silent treatment. This is classic passive-aggressive behavior that is aimed at ignoring the issue instead of working together. A healthy parenting relationship of any point is based on being able to be open. When one person resorts to childish behaviors, the entire relationship can suffer.
Another thing that you can do in these cases is make sure that your parenting plan is as detailed as possible. This takes away the need to deal with your ex very often since everything is going to be right there for you to review when you need to know what to do.