Uh, I'm not an attorney, but if the father is living (although comatose) isn't there a legal presumption of the possibility of recovery? So while the kids' placement would very probably go as people have suggested, unless the father also dies his will isn't going to enter into the equation.
My god, I can't believe I didn't notice that detail!!!
You're right, of course; the father's will might as well not even exist until he dies--it has absolutely zero legal effect until he's dead.
But the mother's will, of course, kicks in as soon as she dies. Presumably each parent would have put something in there about what they wanted to happen to their children in case of death. So, the court will look at what the mother wanted--and there's some possibility that the court would consult the father's will just to see if it agrees on that point, although the court is under no obligation to do that; it's just that, if that's the only written record of what the father would have wanted for his kids, they might look at it. It would have no legal weight at all in and of itself, but the court might be able to consider it if there were no other evidence of what the father wanted.
But, yes, if the father's still alive they're not going to give permanent custody of his children to anybody. They do still have to figure out what to do, of course--i.e. who will be the legal guardian of these kids. They'll make someone their legal guardian, and that order will stay in place until/unless the father comes out of the coma. (By the way, they'll also have to appoint someone to be guardian of the father, since he can't manage his own affairs while he's in a coma: someone to pay his bills, handle his assets and so on.)
If the father is alive, however, I highly doubt the court would give guardianship of his kids to someone who lives overseas; for that to happen, my bet is that (1) the overseas guardian would have to be closer to the kids and provide a better environment for them than any possible guardian here in the US--so this might happen if, say, the parents were from another country and had little or no family here, or if what little family they have here just didn't have the resources/desire to care for the kids; AND (2) the foreign country would have to be a signatory of whichever convention it is that makes countries cooperate on child custody issues (i.e. the judge would have to be sure that his/her custody order would be respected by that foreign country's courts: if he gives temporary custody of the kids to the guardian pending the father's recovery, and the father recovers, the court needs to be sure that country's courts will force the guardian to give the kids back). If you're talking about a western European country or Canada, no problem. I think Japan may also be a signatory, though I'm not sure. But anywhere else, you may have a problem.
When the father wakes up, presumably someone will inform him of what's happened and where his kids are; if he's okay with the arrangement it'll stay in place, but if he objects--say, if he wants the kids cared for by someone else--there would need to be a hearing. However, it's still going to be the best interests of the child that the court looks at the most; the father's desires aren't going to overrule a court order for guardianship unless/until the father is seeking custody himself. Obviously, if he's just woken up he won't be very functional; even if there's no brain damage, after three days of immobility your muscles start to atrophy, so if he's been out long enough for the court to have given guardianship of his children to someone else, you can bet he will need extensive physical therapy to recover anything like his former abilities (walking, caring for himself etc.). So it's going to be a while before he could seek custody himself.