The thing about a ski vacation is that you will ski several days in a row and that's not usually the way we do things. So, yeah, don't ski all out the first day! We just got home from our first trip away from our "home base." The elevation change wasn't quite what you're about to experience, but it was a bit higher.
(hydration -- I screwed up here, big time. I blame this on DH, who gets impatient with anything that reduces time moving on the hill)
DH whines about the whole idea of the "kids area" -- at Grand Targhee, they have this cool area that is designed with kids in mind. 500 vertical feet, lots of groomers, a beginner terrain park, tree areas, just generally FUN to ski in. The lift was slow going (THIS is why DH whines about this area -- see above), but the runs were just right when I was getting tired at the end of the day, but really didn't want to go in yet, or at the beginning of the day, when I found I needed to work out the kinks after skiing all day the day before! (sunday, I was playing with demos, and didn't want to take them back at all much less early. Monday, I was paying for Sunday!)
Take advantage of that beginner area!!! We alternated some -- a long, challenging run or two, then some easier stuff. It will also help for getting used to different snow. We also found that there were a couple of in between lifts -- one about half the total elevation, and one somewhere between half and total. I bet you'll find that at Alta too.
OH! the hot tub when you go in! INcredible help with the muscles! And, the base layer under whatever you wear all evening too -- that helped keep my muscles loose for the next day...
Kano