I would recommend going with flying out of Burbank and using the Amtrak
Pacific Surfliner Train. Burbank would definitely be less of a hassle for your
family then LAX. Considering that September 1st is a holiday traffic might
be a factor and driving could take between 45 minutes to over and hour. Also,
Train #769 which is the 12:47pm arrival into Burbank is usually on time and with the airport being easy to navigate, one hour is still enough time to make
your flight. Otherwise, to LAX you would need to hire a shuttle service to the
airport or take the Amtrak to LA Union Station and hop on the FlyAway bus that departs to LAX every 30 minutes.