Is it permissible for someone who vowed to join a Quran memorization class after recovering from illness to memorize at home instead of going out to the class, and would she incur any sin by doing so?

Allah has made fulfilling vows obligatory and praised those who fulfill them. The Prophet, peace and blessings be upon him, commanded the fulfillment of vows if they entail an act of obedience. A vow conditional on something other than a sin is disliked, yet fulfilling it remains obligatory. If the memorization center is close or a mahram is available, she should go to the center. However, if there is hardship, difficulty, or a religious prohibition involved, there is no impediment for her to continue her memorization at home, using audio tapes or with the help of mahrams. For one who makes a vow they cannot fulfill, the expiation for breaking an oath is sufficient.