Madam_Butterfly,
You are writing quite well -- we understand!
In addition to what jennybebooper wrote, since you are in the UK (Britain, Scotland, Wales, or N. Ireland), I assume your medical coverage is covered by UK's National Heatlh Service. I think more serious for you will be the time from family & work to go through the evaluation process -- and, if you donate part of your liver, the time needed for recovery, in which you will not be able physically to yourself take care of your 3 & 5 year old sons. Also, if you and your partner are thinking of having another child, you should take with the Transplant Center about how a living liver donation may affect child-bearing.
You also should know that donating part of a liver is more dangerous to the donor's health, and with a higher chance of severe or long-lasting complications, than is donating a kidney.
If you can stop smoking now or soon, and stay off smoking through surgery, the surgery will be easier. Unless your prior drinking caused liver damage, social drinking (one drink a day for women) even at present is usually not considered a health problem that would disqualify you from donating.
As jennybebooper wrote, please speak to the Center concerning your medical history. In addition, I/we encourage you to ask the Center to give you the name of one or more living liver donors, to learn from them their own experience of the evaluation and then donation surgery.
Bill