Is it permissible to abort a fetus in its third week with the agreement of both parents due to difficult circumstances such as living abroad and the young age of two other children, and what is the ruling of Islamic law if the abortion is carried out?

It is not permissible to abort the fetus before forty days except in cases of extreme necessity, and what is mentioned in the question is not among these necessities. Since the abortion has occurred, the questioner must repent, seek forgiveness, and resolve not to return to it. It is worth noting that it is not permissible to abort the fetus after forty days have passed unless there is a real danger to the mother's life.