It would be a lot easier for you if you could spend one night in the park, because doing 10 hours of driving in one day will leave you exhausted, and you won't have too much time in the park. But if you can't stay overnight, yes, you can do what you plan.
Long Beach to Visalia is 212 miles, with a driving time of 3.5 to 4 hours depending on traffic, plus any time spent at stops along the way. We usually stop at the Pyramid Lake Visitor Center (Vista del Lago exit on Interstate 5) for the nice large clean bathrooms and the exhibits about water usage, although there is no food sold there, it's a good place to stop and stretch your legs. Then continue north on Interstate 5, but get on California Highway 99 north to Visalia. From Visalia to the park entrance is about 45 minutes, then maybe another 20 to 30 minutes to the Giant Forest area.
If this trip is going to be in the summer season, there is a shuttle bus from Visalia up into the park, and it's only $15 for a round-trip ticket. See …visalia.ca.us/depts/…default.asp for more information on that shuttle. This year it operates from May 24 through September 9.
The drive on Highway 198 from Visalia up into the park has over 100 curves, I think. If you are prone to motion sickness, take Dramamine and/or ginger pills before the trip up the mountain, and try to keep your eye on the center line of the road. Usually the driver of a car doesn't get motion sickness because they are paying attention to the road, so what they see is in sync with what they feel.
For the exact times of sunrise and sunset on the day you want to do this trip, go to http://sunrisesunset.com/USA/NationalParks/ and from the "Select a location" menu, choose Sequoia - Lodgepole VC, and then choose the month you will be there and click "Make calendar" to get a calendar showing the times of sunrise and sunset. Catalina is nice, but Sequoia NP is better, in my opinion.
Edited: 2:35 am, July 14, 2012