This sounds tactical to me.
Married or not, they are his children and he has a legal (and moral) obligations re: maintenance.
This does not change because he doesn't like your new address, maintenance is NOT an optional payment.
If he wants to make an application to the court in respect of child care arrangements HE will have to pay to make the application.
As Fourormore said you could, if the worst happens, self represent IF an application is made.
There is no rule to say that you have to use a Solicitor. And there are lots of great organisations out there to help along the way.
I capitalised 'IF' because threatening to take someone to court and actually doing it are very different things.
Lots of people threaten to do it and when the reality, and costs kick in, change there minds.
The children are the priority, as they should be, not the proximity of where they live in relation to there dad.
As long as you have been reasonable in trying to sort things out re: access you should be ok.
Hope this helps