I am speechless Aimsmum, what an absolute wanker he is.
However I think this is a perfect example of what I used to come accross all the time when I worked in a Contact Centre (for children seeing absent parents) - when things are not amicable between the parents, the contact must be kept purely and simply and only about the child seeing it's parent. No progress toward good relations can be made when the parents use the contsct time to pass notes about bills, finances, or other 'adult' matters. As others have said the child simply ends up in the middle, feeling all the anger and conflict...
And due to your ex being such a prize pillock I'm afraid this is where you are at the moment - his contact is mixed up here with your social arrangements and that's where the conflict arises. GOD KNOWS you SHOULD be able to arrange something this simple with his help but obviously he is still angry and bitter and using this against you, he's just not 'there' yet unfortunately.
Personally I think you will have to rely on others to be flexible about arrangements like this, as your ex simply cannot cope with it. Maybe one day he will get there, I certainly hope so for your DD's sake as well as yours!