You and your children will have fun! But even without a car, there's so much to do around the Hyatt in San Diego where I have stayed myself, and check out some hotels that do have complimentary shuttle transpo to the amusement parks. Ask Hyatt for any recommendations before you go (email). But you are right in that staying near the amusement parks would be better, specially in such a sprawled out place like California where driving cars is the main transportation (although buses do exist but I never needed to use them because I drive instead).
Also, you might be needing some required safety roadway protection in California like "booster seats" for your kids (minimum 40 pounds) if you are in a moving vehicle...it might be hard and expenisve to find a chauffeur-driven rental cars you were planning - usually it's just a limo that would have such a driver and it is expensive (per hour) not mentioning the tip. Being Asian myself, I know this is so unlike in other Asian countries where drivers are easier to hire.
Enjoy your time in California - it's a great state and people will be nice and love kids...


