Is it permissible for a husband to reclaim from his divorcée the expenses of her arrival (such as passport costs and airline tickets) after discovering her bad reputation and dishonesty, which almost led to the breakdown of his first marriage and the loss of his children?

If you divorce your wife after consummating the marriage, you have no right to take anything from her mahr (dower) except with her consent, due to the Almighty’s saying: {And if you want to replace a wife with another and you have given one of them a qintar [a great amount of wealth], do not take anything back from it. Would you take it in injustice and manifest sin?}

As for the money you spent on her travel and relocation, if it was a condition upon you or customary practice, then it is binding upon you. If it was not a condition or not customary practice, then it is not binding upon you. However, if you paid it and did not intend to reclaim it, then you cannot demand it back. The summary is: "retention with fairness or release with kindness." In case of dispute, the Sharia (definition) court will decide.