Is it permissible to give charity on behalf of a daughter, instead of her fasting the remaining days of Ramadan, given the difficulty of fasting due to a prolonged and irregular menstrual period and her taking multiple medications?

If the blood flow exceeds fifteen days, the woman is considered to be in a state of istihadah (non-menstrual bleeding) and must observe the rulings applicable to a mustahadah. As for the days your daughter missed, she must make them up before the beginning of the next Ramadan. If she delays making them up without a valid excuse until the next Ramadan begins, she is sinful and, in addition to making up the days, she must offer fidyah (expiation) by feeding one poor person for each day. However, if she had a valid excuse due to illness and her illness continued until Ramadan began, there is no sin upon her, nor any fidyah. Instead, she is only required to make up the days when she is able to, and the expiation is not waived as long as there is hope for her recovery from the illness.