Does the divorced husband have the right to control his ex-wife's return to her home country, or does the decision rest with her and her family, taking into account that her return might deprive him of seeing his daughters, and her remaining might leave her without a mahram?

If you divorce your wife and her 'iddah (waiting period) expires, you no longer have authority over her, nor do you have the right to compel her to travel or to remain in that country. Her remaining there does not require the presence of a mahram, but rather safety from fitna (temptation/strife). The custody of young children belongs to their mother, unless there is an impediment. However, if the mother travels to her own country, the majority of scholars hold that the father has a greater right to custody.