I'm sorry your mother had to go through this experience. You possibly have a legal claim against Delta. Airlines have a responsibility to take reasonable measures to protect their passengers from other passengers, and if they failed to do so your mother can be compensated for her injuries. Your case would hinge on whether of not the Delta crew and had notice of the drunken passenger's condition and actions. And based on all that you wrote, it certainly seems that the crew was aware of the passenger's condition and actions towards your mother and other passengers.
How much your mother could possibly be compensated is really the question here. Certainly I believe she would be entitled to a refund for the cost of the flight, and perhaps a few thousand dollars for the experience she has to endure. If she suffered any lasting physical or psychological injuries, then the compensation could rise significantly.
For these reasons, perhaps sending essentially the same letter from a local attorney demanding a specific amount you wish to be compensated for would be worth your while. The letter should contain a warning that a civil action
will be commenced if your mother is not compensated.
In addition, your mother would clearly have a civil and criminal claim against the drunken passenger for assault and battery. And perhaps that is another avenue you may wish to pursue. So, in your communications with Delta you should ask for the name and address of the drunken passenger so that a possibly criminal complaint
and civil action can be brought against that passenger.
A letter from an attorney is likely to get more attention. But of course you have to weigh the cost of hiring the attorney against how much you wish to be compensated for.
Again, I am sorry your mother had to endure this experience, and I wish you good luck.