According to the OP he was worried about the family emergency that evening (fair enough) but as it was his day off 'caught up on sleep' the next day, until 5pm. He can't have been that worried about his brother, never mind his step-child, or in fact his actual child, or the OP, if he managed to sleep all day instead of offering any kind of support whatsoever
He must have got the phone call from his brother after 11pm when he finished speaking to OP so he may have got to bed very late following a late finish at work working to difficult phone calls, in those circumstances I could easily sleep through until at least early afternoon. He may have been awake for hours stressing, leading to him sleeping late, as well. He may not have meant to sleep in that late. I don't see why him sleeping late is considered proof he wasn't that bothered, it could easily be a result of how bothered he was.
And @Clymene it is confusing because OP has written in a scattered manner. The OP was also written like he could be the girl's father and when several people asked, OP kept saying "we have a child together", when in fact that wasn't the child in question. It reads to me like she is twisting things to fit her perspective, either for our benefit, or for her own. With that in mind, and given she doesn't actually say what he said to her when she rang, I do think it is quite possible she is blowing his lack of support out of proportion due to being upset.
That doesn't necessarily mean he has behaved perfectly fine, ideally he would have been there to offer support for his partner at a difficult time. But if he was genuinely very worried about his brother, as many people would be, and he did actually show some support during the first phone call with OP (unclear) then I don't think it is the hanging offence it's being made out to be. Some people are not emotionally strong enough to support others while they themselves are struggling with something they consider equally worrying.
If he was due to have his child and chose not to then he is of course being unreasonable regardless.