Silver Family:
There is nothing harder than letting go when we want so badly to hang on and make everything better. The more we care, the harder it is to let go. I don't know how open you are to all the words of wisdom in these replies, but I hope that time will help you to see that you've already done all you can do.
People make their own decisions and it can be exceptionally hard to stand by when those decisions are self-destructive. But, that's what unconditional love and acceptance is. It is not a condoning of their behavior, or enabling. Rather, it is a recognition that you are the master of your own life and they are the masters of theirs. If you speak with an addiction specialist (which I hope you do, at some point - or take everyone's advice and check out an Al-Anon group) - you would see that no one and no single act can force sobriety. One must enter into sobriety, or any healthy lifestyle, on their own accord.
Try to think about other addictions: cigarettes or food, for example. If you take away someone's smokes, does it fix the problem? If you force someone to eat certain foods, does it deal with the real issue of their binging/overeating? No. One needs to be dedicated to stop smoking - or eating healthy, it can't be forced upon them. Or, think about something easier - more tangible - like deciding to make exercise a regular part of one's life. You can't force cycling or fitness onto anyone, right? Everyone has to take responsibility for their own lives and decide each day, each week, to get out there and put the time into staying healthy. With addiction, it is no different. The responsibility to change falls on the shoulders of the addict.
It is clear that your family is filled with love and wants nothing more than to care for your parents and see them well. But, if your parents aren't joining you in your efforts - you're setting yourself up for a great deal of pain...pain that no one in this forum wants to see you go through.
You can't control them. You can't convince them. And though they are aging, you are not responsible for their decisions. If they want to drink themselves to injury, that's their choice. If they want to make choices that result in being moved to a nursing home, it's their choices that got them there. All you can do is make sure they are cared for and safe - something you are doing a beautiful job of already. They will decide on a life of sobriety when they want it, if ever. Until then, all you can do is love them and take care of yourselves. There is nothing easy about the position you're in, but it is manageable - with the right resources.
I'm glad you came here for support and advice. I hope you continue to do so for as long as you need it. As for the advice, I have always believed we always know the answer to our own questions - deep inside. Advice is what we ask for when we know the answer, but don't want to admit it.
In time, the truth of how much (or how little) control you have in this will become more evident. As it does, and you grow to feel increasingly helpless - I hope you will put your energy into getting professional support for your family. You can't control your parents addiction, but you can control how you and your family handles it emotionally.
I wish you the best of luck with everything.

