I understand your concerns for your mother. Before you start her on medication, you should try all the sleep hygiene
measures. Firstly stop all tea/coffee/alcohol/chocolates/colas as all of them contain caffeine. Next you should start her with daily exercise for 15 min to 30 min. Take a warm bath at night, regularize her sleeping timings. Dont let her try too hard to go to sleep. If she is not getting sleep, sit up, do some reading and again go to the bed when she feels drowsy. Use your bed exclusively for sleeping and keep her bedroom lit dim. Any psychiatric medication will take time in acting and you should avoid switching psychiatrist
in short time. All the medications are good for starting back on sleep and some may suit her. Tryal should not be taken at night. If the problem still persists, please visit some other psychiatrist who can help you.
Hope I am able to solve your concerns.