Is it permissible to supplicate with "O Lord, admit me to Paradise without reckoning," and to ask others for this supplication?

It is permissible for your mother to supplicate for herself with this supplication and to ask others to supplicate for her with it. In the noble prophetic Hadith: "Seventy thousand of my Ummah will enter Paradise without reckoning. They are those who do not seek Ruqya, nor believe in omens, and they rely upon their Lord." And when 'Ukasha ibn Mihsan asked the Prophet, may Allah bless him and grant him peace, to make him one of them, he said: "O Allah, make him one of them." In another Hadith: "May my father and mother be sacrificed for you! If you are able to be among the seventy thousand, then do so."