ok, separate the issues.
1.
children
children deserve to be raised in a loving safe environment. If you are frequently acting out your frustration or jealousy on your step-children then you are probably not the best person to be raising them.
If you love them and want to raise them then you need to work through the issues which most families with mixed natural and stepchildren face. There is advice on
http://experts.about.com/q/2203/
2.
alcohol
many people self-medicate with alcohol and in the short-term it seems to help. But longer-term it causes depression. If you are already struggling to cope and maybe depressed then a better solution would be to see your doctor for counselling and/or antidepressants.
There are two models for dealing with alcohol problems, either learn to moderate and manage use via Moderation Management techniques
http://www.moderation.org/ or abstain using AA or other support ( eg. antabuse )
There is loads of literature on the negative effects on children of growing up around problem alcohol use, so you are right to address this issue.
3.
your relationship
stop telling yourself you cannot cope without this man, from what you say he contributes little to your family's wellbeing and only adds to your stress and distress.
Find out about womens' welfare services in your area, and get support.
4.
you
it sounds like you have lost sight of yourself, and lost hope for your future and are living chaotically.
Start by taking care of yourself in small ways: take a vitamin supplement ( a B supplement is essential by the way for heavy drinkers ) put on lipstick, listen to music, take a walk or other exercise.
Go to the library and check out books on self-care and self-esteem and parenting, or any other books you're interested in. Plan to take some classes in the future.
Try to make a new perspective on things, make budget living a challenge and fun eg
http://www.budgetlivingmedia.com/
Treat it as 'downsizing'...what smart people do to escape the neverending pressures of materialism!
Don't expect everything to change overnight, but start making positive steps towards a meaningful life and you won't need alcohol so much and your children will benefit from seeing mum/stepmum turning things around. You're the adult- take charge.