What is the ruling regarding an elderly woman's recitation of the Quran, given her numerous mistakes and inability to learn? And should she be prevented from reciting or should her mistakes be corrected?

If your husband's mother makes mistakes in reciting the Quran that change the meaning, then she should limit herself to what she can recite well, and listen to the Quran from a live reciter or via a recording. The hadith, "The one who is skilled in the Quran will be with the noble and righteous scribes, and the one who recites the Quran and stutters over it, finding it difficult, will have two rewards," applies to someone who does not change the meaning and hesitates in reciting due to a weak memory, not to someone who makes mistakes and changes the meaning. You must advise her not to recite what she cannot recite well, and teach her the correct way when you hear her make a mistake.