Sounds like your DH has had some very bad luck. I'm assuming you are on a ski holiday, nightmare especially if they are quite young.
If the kids are booked into ski school then I'd make sure they get there. If they are occupied and getting fresh air they will frankly be less annoying when they get back in the evening if your DH is presumably in pain. If you can book them in for a slightly longer day, then I'd try to throw money at the problem rather than try to manage 3 kids on the slopes in the afternoon with varying abilities especially if you are not a really strong skier. If the resort has snow, then lots of snowmen making won't kill them, if it doesn't then if your DH can get to a sun terrace somewhere then it might be time to introduce the kids to card games if old enough.
Car to airport - might be useful to say which resort and airport. Not sure I'd be terribly comfortable putting a complete stranger on the hire car insurance as a way to get back to the airport with all of you in the car so on this occasion, it might have to be left to the car agency to arrange. Add it to the list of things to check in with your travel insurer. A local taxi firm might be worth checking in with, at least you'd know the driver was experienced and licenced to transport people generally. I doubt it's a rare occurrence in the Alps.
Transfer day is transfer day, no way to go home early without racking up a lot of cost. Which airport are you flying from? One option might be to transfer by taxi the night before to an airport hotel. Chambery has one right at the entrance for example - fairly basic but French budget hotels tend to do half decent family rooms. Means you will have less to wrangle out the door at whatever unearthly hour you probably have to leave at on Saturday and you can leave out travel clothes and just pack everything except charging gadgets before going to bed. Put DH in charge of gadgets and making sure the kids have something to watch, headphones etc are fully loaded and you can focus on other things.
Get yourself to the shop and pick up lots of snacks in case of delays. They can be used for school lunches next week if not needed. Airports usually have water stations too.
At the other end, if you can leave some/all of the kids with your DH and take the shuttle to collect a car and come back to the airport that feels like it might work best. You could take a large bag so there is less to manage out to the car in the short window you get to pull up and load everyone in. Otherwise a taxi so you can get some help with bags?
Otherwise, lots of painkillers for an undoubtedly grumpy DH and wine for you. Picnic meals if you are in self catering. No child ever died from eating too many simple ham baguette and rotisserie chicken dinners.