If your XH is arrogant and controlling...

[CommonBurdock]

How do you deal with it calmly without spending thousands on lawyers?
Things like refusing to be flexible on DCs flights so they can't see their grandparents, blaming me for absolutely everything and generally being a controlling arse because he's angry that I dared leave him (for being a controlling arse)?

Pick your battles, stay out of contact as much as possible and anticipate he's going to be awkward to avoid disappointment. Rest of the time, steadily clip his wings and reduce the amount of things he has any influence over.

Don't expect anything from him, particularly good will.
Assume he will do his best to make life difficult for you, so work around that. You can use reverse psychology.
Ignore his rants and respond only to what concerns DC. Be factual and straight to the point.
Do not bend over backwards or be the nice one. He will just take advantage. Be selfish and stick up for your children.

draft in a family member to liaise. For years, my x and I didn't communicate at all and it was great because he didn't used to subject my parents or siblings to the same antics he would have subjected me to. He was forced to behave like a normal person (or closer to one). He was never exactly compromising but he didn't tantrum so aggressively if we didn't capitulate instantly.

All good advice thank you. Problem is we have shared custody with the added joy of frequent travel on my part, so the opportunities for him to make life difficult are many and varied. Still, he is the pedantic type so I'll just have to get it all agreed in writing in advance.

Keep communication to writing and very brief/factual - avoid face 2 face negotiations or over the phone discussions. Employ the 24 hr rule - don't answer any request for 24 hrs; that gives you time to think; be as repetitive as you can ie have the same answer to the questions even though they are posed in different guises - be highly consistent and don't back down. If you are consistent; implacable and stone walling they do eventually get bored and leave you alone.

Keep everything in writing. Do not engage verbally at all, or if you can't avoid it make sure you minute it and send him an email reiterating everything which was agreed.