Take a deep breath, Is. We all seem to make colossal mistakes as we try and deal with the reality of our situations. You screwed up a bit, true. But, on the plus side, she was drunk. I really mean that. She's going to remember some, but not all of it.
Exchanging phone numbers with a taxi driver right outside your home is disrespectful. You have a valid point with that. It's not just the exchanging of the number, she was out there for a while, and you were worried. You overreacted a bit. She is highly emotional because of her dad.
Apologize when she gets up. Just let her know you were worried, and overreacted a bit. Don't talk about much else until you get a handle on how much she remembers. Let her know you are there for her. You understand how much her father's failing health is bothering her.
Talk to the kids, and let them know everything is all right. You were worried, and overreacted. The last thing you want is for them to bring it up to her if you can help it. Tell them you had a bit of an argument, but everything is fine right now.
It always feels like the end of the world when you make a big DBing mistake - but it's usually not. Just go back to doing what you know you need to do. Your situation is unusually tense at the moment with FIL being so close to dying. That's hard on anyone.
