A bit of background. Ex husband and I have 3 children together. We are divorced and split over 10 years ago. He is now a millionaire and was able to advance his career in part due to me doing the lion's share of everything relating to the children. I work full-time but earn a fraction of what he does.
Ex husband cheated on me, hence the breakdown of our marriage. I was dignified throughout and always wanted to be friendly for the benefit of the children. He has always been very cold towards me and can barely look at me when we meet. We're civil but it's clear that he has absolutely no time for me as a person. Fine. I've always tried to be the best mum I can be to our children. Not perfect by any means, but I try to be present and good.
Unfortunately our middle daughter has developed a lot of school-based anxiety. I am liaising with school to develop strategies to help, but it's clear she needs some extra professional intervention. I have found a clinical psychologist for our daughter and have forwarded my ex the details. It's not cheap. But our daughter is at crisis point, and has been offered an appointment for this Sunday. Daughter will be with ex husband on Sunday, and I wanted to be sure it suited him before confirming the appointment.
This was his reply to my email:
Sunday is fine, to be clear you aren’t making a contribution?
No hello, no thanks for sorting the appointment, no warmth whatsoever. He clearly doesn't find the cold approach tedious after all these years. We hadn't discussed payment of the sessions, as I find communication with him so difficult. He can be challenging and very passive-aggressive. I probably had hoped he would pay, if I'm honest, but am happy to make a contribution.
He wouldn't speak to a member of his workforce like that in an email, so why is it ok for the mother of his children 
How should I reply?