Day 1: Parked at Agnew meadows and hiked to Shadow Lake. Camped overlooking Shadow lake. Did some side hiking.
Day 2: Took JMT to Thousand Island Lake. Passed Garnet Lake, Ruby Lake?. It was the JMT so the trail was pretty easy going. We then explored around the lake after setting up camp. We did take a quick dip in Garnet Lake to wash off the dust. It was quick.
Day 3: Left camp setup and took an early morning hike up to Lake Catherine. Around Thousand Island and then off trail up to Lake Catherine. Terrain was mixed: faint trail, boulder hopping, etc. We then back tracked to Thousand Island Lake and hiked back to camp around the other side of Thousand Island. We then packed and head over on spooky meadows trail past Clark Lakes, etc. We setup camp beside a no name lake. Had two camp options: 1) in a bowl with protection and 2) on a nice clearly with excellent views.
Day 4: 3:30am start. We left camp setup and hike a fairly strenuous off trail path to the peak beside Carsons Peak (probably a 15 min hike from Carsons). We were going for a sunrise view and ran out of time to make Carson. Really cool watching the sunrise and drinking a hot cup of coffee/tea. The hike was interesting because the first was real steep from the lake up to a plateau (45-60 min hike). The next hour was across the plateau with a little elevation gain. The terrain felt almost sandy (beach like) which was really cool. We then back tracked to camp and hiked out spooky meadows to June Lake area. We had a car parked for the trip back to the starting trail head.
Since I'm an East Coast (NC) guy, I always use Neil Satterfield from Sierra Mountain Guides to lead our trips. He is an excellent guide and we have used him 4 times and will again next year. I feel confident I could lead a trip in the area, but Neil does all the coordination (permits, etc) and knows all the good off trail spots.
Looks like you and your daughter had an excellent trip also.