Delta serves Long Beach as well but has limited flight options (3-4 daily to Salt Lake City).American Airlines no longer flies in/out of there. I think it’s solely southwest now.
Long Beach is easy in, easy out but it’s only 20 minutes south of LAX on the 405. The flight options presented by the OP will have their family traveling when traffic volumes are light. The best option is to go with the direct flights to/from LAX.
Things can go wrong no matter which flight option you choose but when possible it’s always best to go with the direct option that has the most frequency. For Fourth of July, we traveled SNA-CLT-MCO on AA and the CLT-MCO flight cancelled (after we boarded it). Next available flight accommodating our family wasn’t for 24 hours, and we tried unsuccessful to standby for earlier options. Expensive, too - AA had no hotels, the meal vouchers barely covered a bottle of water, we had to pay for one night’s lodging we missed and we had to rebook our rental car for $400 more over two weeks.
And now you know why I go out of LAX when SNA is 10 minutes away . This was our second blown connection in 6 months (coincidently both on AA and at the same airport).
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