Maintenence from spouse in USA

Hi.
Not posted for a while.
My partner, a dual national, moved over with her daughter(4) from usa to england 18 months after her marriage ended. She also has a son(10) who opted to remain in the usa to live with his dad. So now there's a child on both sides. This is difficult emotionally and financially.
From my perspective i have taken on this lady and her daughter and i accept that responsibility. My salary is enough to keep things ticking over. I have 3 children of my own prom my previous marriage whom i love, see regularly and financially support willingly.
But this chap in america is slightly less obliging. He is prepared to buy toys and gifts for his daughter, school uniforms and ballet lessons. He is prepared to pay for her airplane tickets. He is prepared to fly over every year to spend time with her. He's a good dad. He ended his marriage by having an affair with his boss and subsequently setting up with her.
But he's not prepared to commit to send any money on a regular basis.He lives in the former marital home and to date has not formulated a plan to separate the assets of the marriage.
So basically my girl and her daughter are being supported by me. I pay for her to fly over to see her son and take care of the household bills and stuff. But i'm working very hard to make ends meet.
we're poorer than him and his new partner. My girl is planning to start work in august when the daughter starts full time school.
From her ex husbands perspective, they look after one kid each so he pays for the boy and she pays for the girl. Except she's got no income.
Is this chap obliged to financially support his daughter in view of the fact that he has custody of the son? We suspect perhaps he is and i think he suspects that perhaps he isn't.
Have to be very nice all round to keep this situation going and don't want to fall out with the american side over money. But financial obligation and settlement are a part of divorce and this is the divorce forum. So i come to you.