I hiked a similar itinerary last September, but in reverse and with a variation. I'm a young buck myself, but my companion was (is) getting over a chronic health condition, so we took it easy.
Here is my (very brief) trip report.
We entered and exited at different trailheads, but it wasn't a problem. We left our car at Dog Lake parking and took the Tuolumne shuttle bus over to Murphy Creek. It cost a few $, the driver was friendly, and there was plenty of room.
Entry: Murphy Creek T/H. We got here about 11 am, if not later, and still had plenty of time for the first day's hike.
Night 1: north side of Tuolumne Peak. The difficulty of the hike is similar to Young Lakes, but with the advantage that if you don't make it all the way you can legally camp in the forested basin behind Polly Dome. If you do make it, enjoy the two little lakelets (not shown on all maps, and the higher one is a bit of a secret, but they're definitely there). Right where the trail crosses over the ridge from the east face to the north face, you can climb onto a low granite knob with near-panoramic views.
Night 2: Glen Aulin. Take your time getting here... it's crowded.
Nights 3, 4: Young Lakes. Just as a note, I found the climb up to Young Lakes from the south much less pleasant than the eastern "main entrance", but it's on your proposed itinerary anyway, and of course Young Lakes is worth it.
Exit: Dog Lake parking