I can think of a situation where the ex wife paying for everything makes sense. Keep in mind that
@Passionate1! said earlier in this thread that he didn't ask his gf (Passionate's sister) to attend the funeral.
First of all, he shouldn't have had to.
If my family member dies and I say I'm going home, I'm expecting her to say "what time we leaving?" Or if she can't go, say something like "baby, I wish I could be there for you, I'm sorry that I can't go because of xyz."
Sounds like he wasn't getting no support from the gf at all. And then it sounds like he and his ex wife and the children all needed to go, so they were talking back and forth to work out the logistics.
And I can see the ex (if she's a woman who knows how to plan) saying something like, "instead of us getting separate flights and all of that, I'll just buy our tickets since we all going to the same place."
And I can see him saying "that makes sense. I'll pay you back."
For logistics reasons, that makes all the sense in the world to me.