It's difficult. Assuming that (DHs aside), you and she are equally keen to see each other, it makes perfect sense to split the cost of those visits. Even then, you're still giving more - of your time and energy in travelling.
The problem is that it's ingrained to see that the person getting the 'experience' should pay for it, even though the experience is onerous travelling and staying in a hotel because you're far from home rather than for a holiday - and the fact that you're doing it for your combined good. You've had to physically hand over money at the petrol station and the hotel, so it doesn't occur to them to reimburse half of it as they haven't directly incurred any costs.
It's the same principle as when people automatically leave the car driver to pay for petrol on a journey benefiting everybody travelling in the car (or even if the driver is doing a favour by taking somebody somewhere the driver doesn't need/want to go for themselves) - and then also pay for the parking (airport drop-offs in particular can cause real ill-feeling here). Unless it's a really big trip or a regular thing, the driver feels awkward asking for an equal share of the petrol as everybody assumes that, for the privilege of doing the driving and having to run and maintain the car, they should also pick up the whole fuel bill.
Somebody I know (very much an adult) was driven by her DF to a shopping centre with a time-limited free car park (no option to pay for any extra time). He gave up his time and only went to take her, having no interest in shopping himself. She didn't watch the time and spent too long, so they overstayed, and he got whacked with a huge parking penalty. His bill, of course, though, as it was his car....
I think the only solution is to establish for sure with her that you both and your kids are equally eager to see each other and, assuming that is the case, negotiate by stealth.
Ask if you can meet halfway, as it costs you a lot in petrol and you always end up having to pay for fuel for the whole journey. Point out that petrol will then only cost each of you £XX rather than you alone having to pay £XXX.
When she says she/the kids can't do that, spell it out and say that you don't mind having to do all the driving and staying overnight away from your own home, but in total, it costs you £xxx every time you get together, which is a lot to have to pay. Kindly say that the cost as well as the travelling all falls on to you, even though you both love getting together, which doesn't really seem fair (or sustainable) - so does she have any suggestions how you can manage to continue meeting as frequently?
Maybe she currently sees it that you all get to have a lovely family mini-break (whilst they're just stuck at home) and, as an added bonus to your little holiday, you also get to spend time with them, which costs them relatively little money for food and drink for you all. It might be a silly question, but does she clearly understand that the sole reason you're travelling and paying for the hotel is to see them and because they can't/won't ?