People are being very unkind here. The OP's children shouldn't have to move house again so that their Father doesn't have to pick them up 3 times a year.
If the OP has been advised not to have direct contact with him due to his behaviour, then he must be a real charmer.
I cannot get my head around all these people who say it is important to facilitate contact with someone who is behaving unreasonably. He moved and cut maintenance at the same time, his wife could take them without being put out at all but refuses. It frankly strikes me that this is all about controlling the mother.
These are not the actions of a man who is putting his children first. If he wanted to see his children, he would come and get them.
I am from a blended family and there are 3 fathers in our set up. My own behaved really badly always and I wish that I had never had to see him as a child, I would have had a much nicer childhood without him playing games and he was very controlling. I was walking on eggshells around him permanently. He paid no maintenance and someone else always had to do the transfers.
2 of my other siblings' father stopped seeing them when the youngest was 5. Contrary to all wisdom here, they didn't care and have grown up to be very well adjusted. They knew he had no real interest in them as he had never shown any when he lived with us, let alone afterwards.
My DSF on the other hand is lovely. He has been a real father to all of us and has never shown any difference between his full children and his step children. He was also divorced with kids when he married my DM and we have all blended really well. He took a full part in his DC's lives, he ex wife plus new husband came to the wedding and we regularly have family events with everyone included and no awkwardness.
I suppose what I am trying to say is that a reasonable person wouldn't behave like OP's ex.
As for those posters who claim that as the Family Court agreed the reduction of maintenance, then it must be fine, I really hope you are never in the position that the OP is. The Family Courts are not infallible and, just like the CMS, seem to believe that children cost very little.
The OP may or may not be careless with cash (and that wasn't the AIBU in any event) but in her position I would rather spend what I had on my children on a train fare to facilitate contact with someone behaving like this.