I don't think you can liken the two situations, though, @TPOD74 - you pay maintenance, the OP's ex does not. You make plenty of effort to see your dc, the OP's ex can't even make the effort to see his children when he is in their home town. Your ex wife moved your children a long way from you, the OP's ex moved away from his children.
The two situations are so different that I don't think you can draw any parallels. The OP's ex sounds like a dead beat dad who doesn't care about his children - you sound like a dad who really wants to see his children and really cares about them - you and he couldn't be more different!
In the OP's situation, and given her specific circumstances, I cannot see that it is fair or equitable for her to have to share the costs of contact, whereas in yours, it might well be.
She is bearing all of the costs of raising the children, with no help from her ex, and it sounds as if she is just about managing to make ends meet - I don't think there is much, if any, slack in her budget. Her ex decided to move 6 hours away - it can't be any surprise to him that it is harder and more expensive to get to see his children. It doesn't sound as if he has any real financial problems - he clearly has enough money to live on, without having to claim benefits - the OP has said he isn't eligible, and has money in off shore accounts. So I can see no reason or excuse for him not to make the effort to overcome the distance HE has put between himself and his children. If he doesn't want to use his own financial reserves for this, he could get a part time job, to cover the costs. He has chosen to do neither.
To summarise - the OP's ex seems to have no major financial issues or constraints, whilst the OP has very real financial worries. It is his choice, not hers, to be so far from his children - so he should pay the costs of visitation - in my opinion.