Our first day skiing on our trip at the end of March will be a Sunday and I was wondering which might be the least crowded? Also, is there a shuttle between the two? We are staying at The Resort at Squaw Creek.
What levels of skiers? If you're experts, either one; if you're intermediate/advanced, you'll probably find more space at Alpine.
The Resort at Squaw Creek is very convenient for skiing at Squaw. To get to Alpine you'll have to take either the resort shuttle or the Mountaineer (a great free, on-demand ride service within Squaw) to the base of Squaw, and catch the shuttle to Alpine there.
Keep in mind, If you're at squaw creek without your own car; you'd have to double shuttle over to village then Alpine which will eat up a lot of time. If you drive over, you maybe sitting in the parking line, then have to get from parking lot to the base, which eats equivilant amount of time.
So, if maximizing skiing is your goal, you might as well stay at Squaw, because the transit time loss is going to be more than the time lost to crowds.
So one possible plan for you, since you're at Squaw Creek , you should be ready to go for first chair and then ski your heart out until around 10 when the crowds really start to come....if it gets crowded then take a break at 11, go have lunch in one of the real restaurants or even go rest in your room. Then you go ski from ~2pm to closing and ski back to squaw creek. (Optionally ski lunch hour 12-1 which should also lighten up).
The crowds will be thinned out by then. People will be beating the traffic to get home to SF bay area and get home for a school night. With this seasons' recent Sunday traffic nightmares, more and more people are get beaten into submission to cut sunday short and get out before the crowds.
(note: timing the magic hours is same advice I gave on beating the crowds at northstar in the tahoe thread)