Is it forbidden for a mother not to be proficient in reading and writing, and to frequently forget matters of prayer, given that she was unable to obtain an education in her childhood?

Learning how to pray is not contingent on attending schools; rather, it is an obligation upon every Muslim. The mother must be taught the rulings of prayer as long as she is of sound mind, including the rulings of forgetfulness (sahu). It is not permissible for her to abandon prayer or perform it incorrectly, nor is it permissible for you to neglect teaching her.