Your mother will be considered ma?zoor (excused) if she spends full time of a salah in a condition that the drops do not stop and she does not find a free time in which she can perform wudhu and fardh salah. Then, it is sufficient for her to perform wudhu in one salah time and perform as much salah (whether obligatory and optional) and tilawah she wants. But this wudhu will be nullified when the time of next salah will come in. Then, she will have to perform fresh wudhu. If your mother is not in a condition mentioned above, so she should wait until the leakage of drops stops.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband