Hydrogirl says it all. I'm sorry for your worry for your mother. She is addicted to drugs and alcohol, and your father is in denial. It is tragic, and an increasing problem in this country.
My guess is that at some point her addiction will send her to the emergency room. Your father will likely call you for support.
To prepare for that day, you can begin now to thoroughly educate yourself on the right and the wrong things families of addiction do, so you can make good choices to not enable her or allow her addiction to manipulate you or control your life. You can have a prepared list of local resources--AA meetings list, rehabs, and addiction specialists in her area to pass along to her and to your father, when she is serious about getting help (going to therapy, as she is now inclined to do, is generally just a way for an addict to keep the family off her back and allow her to avoid the hard work of achieving sobriety). Boundaries and information are really all you can do to help. And generally people don't want information unless they've asked for it. You indicate she has opened a small door to getting well. But, as addicts often do, she has closed it up again.
Usually it takes a crisis to motivate an addict to get clean and usually it takes a series of crises. Each one is an opportunity and the family should not try to prevent any crisis, and should intervene only if the addict's life is in imminent danger. Your mother is taking a drug cocktail and should not go cold turkey without a doctor's supervision, as the sudden withdrawal from many drugs can be very very dangerous.
Your mother and your father are both adults and they will make their own choices. It will be painful for you if those choices hurt them. Please know they are free to live their lives however they wish, as are you. Trying to control their lives and choices will create pain and stress in you and with no positive outcome toward solving the problem she has.
Your library will have many books on family addiction and Al-Anon or Nar-Anon meetings are always available. We hope also you will post at SR anytime you need support. Wishing you peace of mind and good self-care.
The Sticky links on the opening page will lead you to further reading.