Ok so here is some really constructive recommendation. Forget trying to sue anyone. Why? well I don't think you have a case, but even if you did you'll be spending a small fortune and for what? You succeed against your sister.
Is she super rich? If not then how much is she going to be likely to be forced to pay you? Yep, not much. The hospital? Well, they have insurance, etc., but they also can afford to pay solicitors heaps and you can't so it will send you broke. Oh and that is assuming you win.
So you wanna hug your kids. If that is your primary objective, then spend your money on a family law solicitor so you can get to see your kids. Make that your priority and if you want advice on that one, then post on the family law section.