G'day!
To answer your specific questions:
Disneyland is in Anaheim, which is basically a suburb of LA. The distance between San Francisco (and therefore to Disneyland) is about 6+ hours.
Here is the San Diego Maritime Museum website. http://www.sdmaritime.org/ They have a collection of ships, which I think that you can tour. However these ships are historic vessels. A naval vessel that you can tour is the USS Midway. http://www.midway.org/
Since you are traveling as a family I think that renting a car would be your best option. It would likely be cheaper than buying tickets (bus, train, plane) for 4 people. And it will certainly be more convenient with the kids. Also, LA is known for not having good public transportation. And if you want to visit the National Parks, it can be difficult if you don't have a car.
Either LA or San Francisco can be a good destination for the adults or the kids.
Near LA you will also find:
Death Valley National Park www.nps.gov/deva
Joshua Tree National Park www.nps.gov/jotr
Theme Parks such as Legoland, Knotts Berry Farm, Universal Studios.
A visit to San Diego also offers Sea World and the world famous San Diego Zoo.
Near San Francisco is:
Monterey/Big Sur to the south on the coast
Yosemite National Park inland www.nps.gov/yose
Lake Tahoe inland on the Nevada Border
Redwoods National Park to the north on the coast www.nps.gov/redw
All of these destinations are a couple of hours to a half day drive from San Fran. But with 10 days you should have plenty of time to see 1 or 2 of these sights.
For ticket information for tours and attractions in and near the ciites, you can go to http://www.partner.viator.com/en/5156/California/d272-vd
Have a great trip!
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