Ok.
Firstly - many congrats on giving the wine away! That's brilliant! So you drank the rest of the gin, well hey, it's only day1. Try to get through a whole day without drinking and just think of how proud you'll be when you wake up in the morning and you'll have gone 24hrs without a drink. Imagine that feeling now and hold onto it as your motiviation for doing just that.
You went through a whole pregnancy without drink and you cut right back during your second - can I just say, that's more than I did! I suffered from ante-natal depression so I did drink lightly during my pregnancies, I was struggling to cope and to give up drink just seemed to be too much to ask. I would have perhaps a pint or two of Guinness over a week. So you can give up the booze, you are capable of doing that. You had an incentive then, the health of your unborn child. Try to place that incentive on the health of your children now, their mental health. They need you as a fully-functioning sober mother who puts them first, otherwise they will suffer and it will affect their lives.
So everytime you want a drink, try to picture that unborn babe who was in your womb, and then project that picture onto them now, still helpless, still needy and totally dependant on you. Try having a large glass of water instead, it'll fill you up and I find that it takes away some of the urge to drink alcohol.
You have bigger issues and they will resurface when you give up, so you do need to tackle those otherwise they'll drive you straight back onto the booze again. Do you think you could ask your GP to refer you for urgent counselling? Is that something you could do? Or, if you like, I'm not a counsellor but I am a good listener. If you want to write it all down and send it to someone, send it to me. I won't break your confidence, I won't judge, I'll just listen and try to understand. CAT me, if you want to talk, if you can't CAT me but do want to talk about it, let me know and I'll CAT you.
You're doing really really well. You've admitted your problem, you've given WINE away! (I'd find that hard!) You are trying to go without booze. These are big achievements, you know, you're not burying your head in the sand, you have the determination to beat this and I'm certain that you will. See this as the start of better things to come! 