Will the husband be sinful if he agrees to his wife aborting her fourth pregnancy - after she threatened suicide and to cause problems - given her inability to bear raising four children in a foreign land, despite his help to her?

If you permitted your wife to abort her fetus at that stage due to her threat to kill herself, then you are most likely not sinful. However, you must clarify to her the obligation of repenting to Allah.

If she herself initiated the abortion, then she owes a "ghurrah" (five camels or 212.5 grams of gold). If someone else initiated the abortion, then that person owes the ghurrah.