What can I do to please my mother, who wishes to return to Egypt because she is uncomfortable living in Saudi Arabia, knowing that there is no one to care for her there, and fearing the sin of keeping her with me against her will?

If the mother needs care and her living with you achieves that, then try to gently persuade her to live with you, and mediate through someone whose word she respects. If she is not convinced, then look for a way for her to reside safely in your country, such as having a reliable maid with her, or having her stay with one of her daughters who visit her and check on her condition.