Welcome to the forum ... this is the place to ask all your questions .. there are some great experts here. I don't class myself as an expert, but have travelled extensively in the US.
For the kids, make sure you have some drinks and nibblies for them in the car.. altho after the flight, they'll probably fall asleep anyway.
The 405 freeway is right near the airport, so its easy to get onto... just follow the signs for 405 SOUTH ... have a look at Google Maps.
My advice for first timers, is to stay in the centre lanes so if the exit is to the right or left, at least you are half way there.
Signage on the LA freeways is amazing ... much better than in Australia .. so if you have to move to another lane, you will be warned well in advance, so there's no problem.
You will find it much easier than you think. As you approach San Diego, the signs are good too for wherever you have to go.
Please remember you can't take your car into Mexico .. and I would really advise you not even think about walking over to Tijuana.
The kids will love Sea World, so I hope that's on the agenda.
Returning to LA, depending on where you are staying next (maybe Anaheim), follow the I-5 freeway north out of San Diego and if you are going to Disneyland, take the exits for Katella Ave/Disney Way. So easy.
I am going to send you a personal message.
Good luck and have fun.