How I understand your question
You have asked about mechanisms to "ensure the return" or something that will "trigger a law-enforcement or legal action if the child does not leave the US on the end of the submitted trip schedule." So I take it as premises of your question that there is a parenting agreement regarding schedule and return, and this trip will happen.
Dale M's answer provides advice about what he recommends to a person in such a situation. However, I recognize that many parenting orders include a term that allows international travel that can't be unreasonably refused by the other parent,1 or that allow international travel with no consent necessary.2
There is no mechanism
There is no mechanism to pre-register a potential violation of a parenting agreement with a foreign state.
I cannot cite to a source to prove a negative, but I am familiar with the operation of the Hague Convention and non-Hague Convention regimes and none that I have encountered have such a mechanism. I have also spent some time looking to see if I have missed something, and am still convinced there is no such mechanism.
1. 2020 BCPC 16: "He shall not unreasonably withhold his written consent to such a trip. If the parties are unable to reach an agreement, Y.N. has liberty to apply for a court order. If the court, on such application, finds that W.G. has unreasonably withheld his consent to such a trip, he is hereby put on notice that he may be ordered to pay Y.N.’s expenses incurred in bringing the application."
2. 2018 ABQB 1031 ("Each party shall be entitled to travel internationally with the children without the consent of the other party upon providing 30 days notice of such travel along with a full itinerary including flight information, destination, where the parties are staying and contact information."); 2010 ABPC 410 ("I will allow T.C. to travel outside the country without the written consent of the father."); 2021 ONCJ 440 ("Either party may travel with the Child outside of Canada during his or her parenting time. The Father requires the consent of the Mother, such consent not to be unreasonably withheld. The Mother may travel internationally with the Child without the consent of the Father, but she must advise him accordingly."); 2020 ABQB 434 ("either party may travel during their respective vacation or ordinary parenting time in Canada or internationally to any Hague Convention Country, without the consent of the other party"); 2017 BCSC 1463 ("The claimant is at liberty to travel with the Children both in Canada and internationally without the consent of the respondent.")