Here, here to everything woooopity has said.
For those who think OP is cold or unhelpful, she had a 14 hour shift in a hospital to get to today. Meaning she has no doubt paid for and arranged child care for her young DS. Not all jobs are easy to just take the day off for. Pretty sure it'd be quite difficult to find someone to cover a 14 hour shift on a Friday at the last minute!
It's just NOT that simple that she was refusing to help, IMO
I'm sure OP probably felt an obligation to her work colleagues and her patients, above all else, also her bank manager, mortgage company, nursery, credit card companies, utility companies, DS, DD's, DP etc etc in choosing to go to her job rather than run around after two strange kids. Perhaps if DDs weren't coping so well, she would have done more, but was happily able to keep well enough out of it, if you discount the emotional turmoil she has no doubt been through this week with her DDs.
And it sets a precedent, how many more times would she be having to bail these kids out (though knobhead ex HAS been bailed out, I'm sure it makes NO difference to him whatsoever WHO did the bailing, DD1, DD2, OP, OP's DP, OP's DSis, he got bailed out, his life carried on the way he wanted it to without a thought for ANYONE else)
There's no doubt about it, Op and DD have had a bit of a bashing from some here.
What I'm not clear on is what happens now? Prodigal father returns when he's good and ready and the childreen are handed over?
Will social services be involved? Will the police not want to pursue abandonment charges? What will happen when the mother gets her flight home (maybe she won't now, though, and stay for the intended period if Daddy has stepped in. Can't see it though)
Hurry up and finish your shift, OP! :)