Just keep in mind, provincial parks are very popular during summer months in the Vancouver/Whistler area, and Alice Lake is one of those at the top of the popularity list. If I was going to give it a try, I would reserve as soon as possible.
There was a controversy this past summer with people/companies block-booking multiple park campground sites for re-renting to out-of-town/country visitors. Although I think that has been somewhat mitigated by changing some of the rules. One of the reasons I initially suggested a private RV park.
Haven't checked so not sure of the quantity/quality of private RV parks in/around the Squamish area (sort of half way between Vancouver and Whistler and in the same general area as Alice Lake).
Marv