The easiest route is the standard Cottonwood-Rock Creek-Guitar-Whitney-Portal via the PCT/JMT:
D1 Rock Creek 12.7 miles
D2 Guitar 9.7
D3 Whitney/Portal 15.5 miles
However, this route obviously doesn't take you by UCL. To do that, you need to go x-c over Crabtree or Discovery. Crabtree has become so popular I wouldn't even really consider x-c anymore, whereas Discovery periodically has some takers who seem to regret their decision.
So, to amend the easiest route outlined above, rather than head down to Rock Creek @ the split junction .7 miles after you enter Sequoia, just proceed straight to Soldier lake, which is 1.7 miles further down the line (for a total of 9.1 miles from Cottonwood pass).
From there, it's easy x-c; in fact, so many people do it, you'll think you're on a trail. SBL is another 2.2 miles, or 11.3 for the day.
The next day, Crabtree pass is approx 1.6 miles and UCL another 2.4. Avg 2 mph, you should be able to get there in 2-2.5 hrs. Hang around a bit, then head down the trail to the meadows, ranger station and up to Guitar, which is around 5.5 miles away, or 9.5 for the day.
If the daily mileage seems to great, simply break the days up into smaller units. For instance, if it takes you most the day to get to LP & shuttle your car, then you could get a late start to Chickenspring. That would make the next day to SBL that much shorter.
The next day, you could head to UCL, hang there for most of the day, then simply mosey down the trail to the meadows for the night. The next up to Guitar would be very short, but would allow you to rest up for the final day hitting the peak and out.
