Is it permissible to admit my psychologically ill mother, whom I personally care for, to a psychiatric hospital by proxy, given the impossibility of bringing her here or returning to her, and would that be considered disobedience?

We advise the questioner to be kind to his mother, to strive for what pleases her, and to avoid what displeases her. For whoever reaches old age with his parents and does not enter Paradise, his nose has been rubbed in the dust. We remind him of the hardship his mother endured in carrying him, giving birth to him, and raising him. And that Allah the Almighty specifically enjoined kindness to the mother, as He said: "His mother carried him, in weakness upon weakness." He must strive for her pleasure, for in it is the pleasure of Allah, and His wrath is in her wrath. We advise him to come to her and take care of her affairs, or to marry a relative who can look after her, while also sending what she and his mother need. If he finds no solution other than placing her in a psychiatric hospital, there is no sin, for Allah does not burden a soul beyond its capacity.