Does seeking alimony after agreeing not to — constitute breaking a promise and entering into the characteristics of hypocrites, and is it similar to the Hadith: "The one who takes back his gift is like a dog that returns to its vomit"?

If your promise to spend on the children was contingent on not sending them to Syria, then it is permissible to retract this promise regarding future expenditures, as maintenance is obligatory for the father. It is not permissible for the father to send the children to Syria if the custodian is not with them, or if the father is not residing there, due to the detriment this would cause to their interests. Parents must consider the children's best interests, and the mother has a greater right to custody unless she marries. Males are given a choice after the age of seven, and females remain with the father unless he is unfit for custody. Fulfilling a promise is desirable, but it is permissible to abandon it if it entails hardship or harm.