It is a dilema, pay and see the kids or not pay and risk not seeing them and then have to consdier taking legal action after that. 

I would consult a lawyer as to the best course of action. One option might be getting the lawyer to send a letter setting out the possible legal consequences should bm not send the children hoping that will scare her into paying. Another option to consider is getting bm to sign a contract which states that she will reimburse the funds and then if she does not reimburse the funds to sue her in the small claims courts for the money. Of course the lawyer could help to write the contract or advise you what needs to be in it for it to be valid. The final option as I see it is to just pay hoping she will pay it back and accept that he will likely have to pay for all transportation costs from now on (this is what my husband ended up doing when faced with a similar dilema, not the best outcome monetarily but definately the low conflict choice). A lawyer might have some better ideas. 

Why do people still use that old "went into the hospital and I have to give them money" excuse?  It is no longer 1973.  Hospitals do not demand cash on the barrelhead for treatment in the US.  If someone presents at the ER with an acute illness they will be treated whether they have insurance or not.  They will set up payment arrangements if the person is responsible enough to want to pay the bill or simply send the bill to collections if they ignore it.  And more likely than not BM's father is old enough to qualify for Medicare anyway which would guarantee care regardless of whether it was acute or a planned admission.  I would bet anything that she is lying based on logic and the previous request for him to pay.

I wouldn't do it. It sounds like their CO was written with lots of detail, probably for good reason. I'm sure when it was written DH knew she would never uphold her financial end of things without it being written into the CO. I'd follow the CO exactly as it is written.

What type of advice were you looking for here OP? Admittedly I did not recall all your previous posts and made ASSumptions about the situation which led to my advice being slightly off the mark for you. I did though try to offer a range of options as people do not always want to take the hard-line approach.

This CO seems pretty well written, why are you seeking advice? What does your husband want to do?

This is all BM's problem. She's trying to put it on your H to help her solve it, but he shouldn't buy into her b.s. She's had eleven months to budget for this, but couldn't get her act together so let her learn her lessons. You guys have a lovely little thing called the CO that spells out how holidays are supposed to go, so simply abide by it. Don't enable BM. Either she finds someone else to use, or she doesn't and the kids spend Christmas with you. Your H should also give his attorney in BM's country a heads up and see what he thinks.                                       

As something wicked points out, I would also be concerned about the circumstances the skids would be in when they are with BM. Do they have a cell phone and a safety plan just in case in the event they do go?

Have you and your DH discussed what you will tell the skids if BM flakes? Be prepared for her to play the blame game when he refuses to pick up the tab for her. Others here can better advise on how and how much should be told to the skids, and in an age appropriate way.

Can't they agree to send the kids without her flying over? Not sure how old SKs are but airlines usually have pretty good service for children under 12 to be taken care off. This would save her money from her ticket and I would just pay the difference in order to get a SK free vacation time.