OP does 99% of parenting, including all the taxi-ing that children require daily.
OP is about to have her CM cut as a result of Ex moving in with another woman and her children (don’t actually get how that is fair or equitable, given that those children have a dad paying CM...)
Ex is demanding the travel is split and OP has to use her own time and money to facilitate his choices.
OP has to do this to send her children into a situation that (based on previous experiences) is highly likely to be temporary and unsettling for her kids.
I think she is putting her kids first by saying no to helping. Ex seems to want everything on a plate. Has ex introduced new gf and kids sensitively? Has he ensured they will have their own space at their new home? Have he and new gf considered family dynamics and how his kids will feel, coming into a new space to find their dad playing daddy to some other children?
There is a massive difference between 2 parents sensitively co-parenting despite divorce and putting their children’s needs first, and a cocklodger who expects his kids to lump it without understanding how it might affect his relationship with them.
I wouldn’t want to facilitate this either. I would be suggesting that, until the baby is bigger, and it’s more clear that this is a long term sustainable relationship, that he comes back to his kids eow and either stays with friends/family or a hotel for a night. Have some time with his kids on his own, without the new family being there. Then, over time, to introduce them in a neutral area and get to know each other. Then build up to nights at the new place.
By this point the OP might be reassured that he’s putting his kids’ needs ahead of his own, and feel more comfortable about helping with the travel.
But that would require the ex to behave like a proper dad.
I’m not a bitter ex, I’m happily with my children’s dad. But I have seen many of my friends tie themselves in knots like this to keep a relationship going for the sake of the kids, only for the kids to be far more messed up by feeling like an outsider in another person’s home, while their dad shows little interest once he’s got them there. What’s worse, not to see your dad, or to see him and it become painfully clear that he doesn’t really have much interest in you anymore and you’re certainly not his priority?
The non-resident parent needs to demonstrate his kids are still the most important thing to him, and the RP should help to facilitate that. But if the ex can’t be bothered then it’s just hurtful to sit in someone else’s house EOW, having had to travel (whoever drives), give up your own activities/parties etc, to be ignored or made to feel unwelcome.