Is it permissible for a husband to allow his wife to travel alone to give birth in her home country, given the high costs of childbirth and the difficulty of caring for her after delivery in the country of residence, knowing that a mahram will be awaiting her upon arrival?

It is not permissible for a woman to travel except with a mahram (a male relative whom she cannot marry) or her husband; this is the fundamental principle. However, if this is difficult, and there is a necessity or an urgent need approaching that degree, such that your wife would be in severe hardship if she remained there for childbirth, then there is no harm in her traveling without a mahram, provided that necessary precautions are taken for her safety. Sheikh Ibn Jibreen issued a fatwa permitting a woman to travel alone by plane in case of an excuse, provided that a mahram escorts her to the airport and another mahram receives her, on the condition that the first mahram ensures she boards the plane and confirms that her mahram relatives will receive her at the destination.