Actually it would be around the lake, not back through Truckee..it is just an alternative way back to Reno.
Phil's alternative route is through Tahoe City, Kings Beach and Crystal Bay, then you'd turn onto Mt Rose Highway before Incline Village. With no traffic, it would be 20-30 minutes longer than I-80 and not recommended if it's snowing as it includes 8900' pass.
Staying at Squaw would be more convenient than Reno, but much more expensive. Even Truckee is a lot more expensive than Reno. If you do stay at Squaw, you do not necessarily need a car to ski Alpine as there are free and frequent shuttles. Any chance you can back up your return a day and use Saturday to ski June or Mammoth or as a travel day, then ski Squaw and Alpine on Sunday and Monday when they and your exit from skiing will be less crowded?
I took shuttle from Grand Sierra Resort (GSR) to Squaw in 2011. It made a longish stop near a downtown casino where I think some people were left as it was overbooked. I don't remember if there was a cost. GSR was the first stop on the way up and it dropped you in front of Squaw's tram. I did not ride it back as friend picked me up. I think there was only one or at most two per day and it is probably hard to get good information about shuttle until ski season.
This link has distances from GSR to Tahoe ski areas although the mileage to Donner Ski Ranch is wrong as it is across the street from one entrance to Sugar Bowl and only a mile or so less distance aussming you take old highway 40.
Grand Sierra Resort also is close to Reno airport and provides free shuttle to airport. It's a huge hotel casino with ~2,000 rooms, 10 restaurants, bowling, driving range and was formerly MGM Grand Reno, Bally's Reno and Reno Hilton. It has a pool and spa, but hours/season never worked for me. GSR is isolated, about 3 miles from downtown casinos and surrounded by big parking lot so even the WalMart across the street is a long walk.
There are shuttles from some of the big casino hotels to Mt Rose, but they stop running March 12
if you can believe this.