Uncorked,
First, welcome to the forum!
I have never been to rehab but watched its effects on my daughter - opiate / heroin addict. Your current attitude shares much in common with her's both when she entered residential rehab and now that she is almost 20 months clean.
I have picked bits and snatches from your story to comment upon:
"..... I wasn't ready for anything to work...." but now you are.
"My life has sucked for some time now..... For many years I've been selfish, self-centered and my world has become smaller and smaller because of my drinking. My kids have suffered...." This is a huge epiphany on your part and makes me hopeful that you are really ready for sobriety - not just because you realize that your life sucks, but because you now know WHY it sucks, that you are taking responsibility for your life sucking and not trying to blame other people or things, and are taking approprite steps to change!
"This place doesn't accept court-ordered rehab cases or anyone under 22. The director said they only accept people who are actively seeking recovery. Don't know if any of that matters." Yes, it does matter, not so much the age requirement but the fact that they do not take court ordered cases. Some, not all, of the court ordered cases will do nothing but drag the facility program down simply because they are not motivated like you are! Slackers, just "doing their time" and taking up space.
"I am sick and tired of the way I've allowed alcohol to affect my life and relationships." There is a saying, something to the effect of "you will get sober / clean only when you are sick and tired of being sick and tired." Sounds like you are there.
I equate going to rehab as comparable to going to college - meaning you will "get out of rehab" exactly what you "put into rehab" -- the same with college. You can skate through college and skate through rehab.
Keep in mind that rehab is not going to "fix" you - that has to come from within yourself. Rehab will offer you a "tool kit" for sobriety, it is up to you as to how well you master the use of those tools. Your long term sobriety depends on keeping those tools well polished from use after you leave the rehab.
"Thank you for reading my story." I would not have missed it for anything, thanks for sharing.
Wishing you the best of luck in your new found sobriety.
Keep coming back,
Jim