Family court appeals are designed to fail because your local appellate divisions provide the trial court everything it needs to settle your case: the lawyer for the child, the psychologists and the visitation facilities. Any appeal will be denied except in those rare cases when an issue is really blatantly obvious and in need of appellate intervention. One example would be lack of service of a pleading.
This is the reason family courts can do anything they want to include taking away your child and making you pay psychologists for "treatment" and "therapy".
As to your particular case, it seems the rule that "the father never gets custody and the mother always loses it" appears to have applied. The ruling is almost never in line with reality and the appellate court will find every possible way to deny your appeal: you failed to frame the issues; you failed to preserve your objections; you failed to make a record; and dozens of other gimmicks.
I'm not sure I understand your question, but I can tell you that a 4-1/2 year old child cannot fly unaccompanied on a commercial airliner. Each airline sets its own rules, but the minimum age on most major airlines is age five. I suggest you contact the airline that would be used to determine that airline's policies. Some airlines have more restrictive policies. If the child has to be accompanied bvy an adult, the cost of the escort is part of the costs of transportation. If this does not answer your question, you need to ask more specific questions.
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