The airport's pretty close to Santa Fe Depot, actually, and your hands are pretty full with 3 kids & all their accoutrements so I'd recommend an Über as the busses & trolleys don't really allow you a whole lotta time at ALL for loading & emarking or disembarking and they can get pretty crowded, not to mention the less than savory clientele aboard. HTH
You can take the Green Line Trolly to Middletown Trolly station go to Pacific Highway and catch the airport shuttle or you can take Uber or Lyft.
Thanks! Your answer is awaiting moderation.