First and foremost, you need help.
Do you have a support network? If not you need to develop one. You cannot manage this without support. It seems like you have been trying to go it alone with your kids, but my concern is that you are all going to go down with the ship. I know this is a sensitive component, but I would suggest finding a local Christ-following church (i.e., generally not a mainline church).
Second, I understand that you, quite naturally, are not sure what to believe regarding matters of faith. Makes sense. But here’s what I want you to do.
In Jeremiah 33:3 it says, “Call to Me and I will answer you. I will tell you great and mighty things which you do not know.”
This is how you can test an see if there is a God and if He is interested in you, on a personal level. Call out to Him. Ask Him to reveal Himself to you. If you do this with sincerity of heart then wait upon Him for an answer. He will answer.
As I read your post, my heart ached for you and your situation.
I went through the responses, and was going to respond to obadiah, and you, but then something of a miracle appeared to me.
God is answering you right NOW. He has placed people from this board in a position to read of your troubles, and many have offered suggestions of ways for you to help your wife.
When I have a problem God always answers me by making one of the tough choices I have glaringly obvious.
I see His hand at work here as clearly as I see the keyboard in front of me.
Faith, my brother. God gives us freewill to make our own choices, but he will guide those decisions every single time if asked.
While you may be indeterminate on God’s actions, I believe others have asked on your behalf, and He IS answering.
Faith will open your eyes to a solution you haven’t see before.