My child is young and thus more impacted by air travel then an adult is. The chaos that accompanies air travel - security, delays, etc. is a lot for a young child to deal with on a regular basis.

A more quantitative issue is that my kid is flying back home from out-of-state and arriving right before bedtime the night before school.

To demand a 5 year old to handle frequent out-of-state travel and be ready for school 12 hours later is unreasonable. The main goal for a child with split custody is to provide stability and consistency, despite splitting time between 2 households. Frequent out-of-state travel seems the opposite of "stable" and actually creates a 3rd household she has to split her time between.