UAE law applies to everyone in the UAE, even for just an hour. The transit zone is still in UAE. You are still subject to UAE law even if you stay on the plane for a very short refueling stop.
A parent cannot issue a flight ban, though a parent could request a government to take an action that has such an effect. Person Status Law 28 of UAE would allow some paternal interference. The English translation of the law is a bit obscure hence the law as translated refers to "tutors" and "fostering". This analysis of UAE law refers to concept in article 142 حضانة (hadana) which is conventionally translated as "custody", but in the translated law article 142 says "Fostering is to safekeeping the child, educate and ward him in a manner that does not contradict the tutor’s right of tutelage over the person of the child" – hence "fostering" is "custody"; then the legal-analysis page refers to ولاية (wilaya – governance, guardianship) in article 148 which is about "tutor". Again, the analysis article says that the mother is usually deemed the "custodian" and the father the "guardian", unless the mother is an unfit custodian in which case the father become custodian. This digression is necessary because of the problem in interpreting what the law actually says.
Now we come to the core law, article 149:
The fosterer may not travel with the fostered child outside the State
except with the written approval of his tutor. Should the tutor refuse
to give his consent, the matter shall be submitted to the judge.
That is, the mother needs written consent from the father.
Kidnapping is a criminal offense in UAE under article 344. According to the analysis article,
if the applicant can satisfy a civil court summary judge there is a
real fear of abduction by the respondent, the judge will order a child
travel ban. They are usually issued to the applicant on the same day,
due to their urgency. Travel ban proceedings are ex-parte proceedings.
The proceedings are taken before the summary court by the applicant
and no service of summons is required. The courts notify the other
parent when the travel ban is imposed.
This provides the legal path for a father to petition the courts for a travel ban. Given all of that, a father could theoretically petition a civil court summary judge that there is a real fear of abduction, in which case airport police might take the child. The main remaining question is whether the father (who I assume is not a UAE citizen or present in UAE) has standing to petition a civil court summary judge (I don't know).
In a case somewhat similar to the hypothetical analyzed here, a travel ban was issued (the father was in Oman, the mother had moved to UAE); then a higher court revoked the ban and the order that the child's documents be handed over to the father, on the grounds that art. 149 and 157 does not grant an unconditional right of the father to veto travel. The court also clarified that the law is designed to protect the rights of a father exercising guardianship duties – in that case, the father lived in another country from the child so was not exercising guardianship duties. This is parallel to the hypothetical case. The Appeal Court upheld that finding.
The summary is that it is possible that there could be troubles in the transit zone, but the UAE courts would not uphold a travel ban.
