The book that really helped me was this one. I would urge you to download and read it today.
I also found it very difficult to sleep without alcohol - my brain would whirr and whirr until 2 a.m. and then I'd be up again at 6. However, even on just four hours I could feel that the quality of sleep was so much better than when I was drinking - but I couldn't face the thought of being up until 2 a.m. every day with my brain going round and round.
Bizarrely, when I stopped (because I had made myself very ill) I found I could fall asleep quickly almost immediately.
I think you've got an uphill battle on your hands here. You're alone every day and thus unaccountable for hours at a time. Your DH doesn't believe you have a problem, which actually isn't helpful. The more people you can tell the better, but only if they're going to believe you and support you.
You'll need to start listening to your brain when it gets triggered. My main one was cooking tea - it seemed so obvious to open a bottle of wine whilst cooking. Another odd one though was getting off the bus, my brain would loudly clang 'wine o'clock' even if I wasn't on my way home from a day at work or anything like that. So you need to stay alert and listen, anticipate those triggers as much as you can. If that means a month of microwave meals so you're not put in the situation of cooking with its triggers (let's say), that's what you do. This has to be the most important thing to you, you must stay committed to achieving it or it's too easy to slip.
You need to stop seeing wine as a reward and start to view it as poison. I hate being around it now, the smell particularly. I never walk through the booze aisle in the supermarket, I deliberately blank it out wherever I see it.
You're right as well that a distraction, both for your hands and your taste buds, is essential. I started drinking herbal teas and ginger beer (not together, urgh) as I needed tastes that weren't too sweet. For my hands, when I was really poorly, I used to play Animal Crossing on the Nintendo, and then as I got better I got into knitting. Now I have an even more ruinously expensive addiction but at least it's not going to kill me 
.
Since we are (in theory at least) in the summer months, can you get yourself out for a walk in the evening once your DH is home? I think you're using wine as a retreat from the non-stop demands of family life, and you need to find other ways to have downtime. If not in the evening I think you and your DH need to prioritise money to enable you to get some free time during the day to clear your head.
I would also advise going to your GP and disclosing your concerns about your alcohol use. This is scary because it makes it real. Your GP may want to run a liver function test (although these can come back in normal range even for heavy drinkers, so may give a false sense of security) or point you to alcohol advice services and support. You need to make this real; it will be too easy to backslide otherwise.
I hope that doesn't sound too scary - you're making the right choice to tackle this before it gets worse.