Without pulling my maps, you might want to consider the Desolation Wilderness area, ending at Tahoe City.
Lots of water in Desolation with some amazing views.
Eastern side of the lake is pretty dry and would require hauling water for some dry camping for the daily mileage you are looking at.
Off the top of my head, the "6 o'clock" position of the TRT to Tahoe City would be the only sections that you would probably look at.
Anything after Tahoe City is going to be gaining elevation and getting drier as you head to the "1 o'clock" position of the TRT, not to mention steep.
Should be an amazing trip for all of you....the children are lucky that you are willing to get them out there to experience it.
Trails are well graded....did the TRT back in 2009, amazing place.
Hope this helps.