BellJar, I can't stop thinking about you and your situation. I am exhausted with my own two sons who are healthy and relatively well behaved. Your exhaustion must run so deep that you don't even know where to begin to get out of the hole. I do know the thou cannot care for your children or your marriage without caring for yourself.
Some ideas would be to start with taking drinking off the table. You see it is bad for you mentally and emotionally. It is also bad for your energy levels, it just zaps the energy right out of you. Do you take vitamins? I would talk to your doctor about this. A few that are usually recommended for energy and uplifting your mood are magnesium, vitamin B, iron and a good multivitamin. Do you have time to take a walk? Try to make time. It seems counter-productive when you are so exhausted, but getting the blood flowing really does help with energy levels and of course will help you start to address those 45 pounds you put on. If you have an iPod or music device, put on some great tunes that lift your mood- there is a thread here about feel good music, or maybe you would like to listen to some Christian rock or gospel songs, whatever gets your head in a good place and helps you escape the madness for a while. Walk it off!
I assume you are being followed by some sort of child protective services people, the folks who helped arrange for the adoption/foster care. Do they have case workers who can come out? I remember when my sons were born we had the very incredible service (thank you socialized medicine!) of an obstetrician/nurse coming to make house visits in the first month. The nurse would come by anytime, day or night. Sometimes she would check on my baby, other times she would look at me and say "take a shower, get yourself dressed and get something to eat, I'll stay with the baby" Is there anyone like that who can come and provide you with even an hour of relief from your duties as mom? Just a moment where you can take a shower in peace without worrying that one of your children is choking themselves?
Another thing, and if you want help with this use message me your location, I'm happy to help google if you don't have time, can you look into any charity organizations? There has got to be something out there for families like yours? Maybe they send you and your family to disneyland for a few days? Or they work with local businesses to provide you with a fun, and paid, day out with your kids. They have been through a lot, as has your biological son, as have you and your husband. You deserve to be helped and/or pampered a bit. Something like "make a wish" but instead of sick kids they help families like yours.
Keep checking in here when you need to, any hour of the day there is someone to listen.
Thinking of you.