Children are not capable of understanding addiction. I would tell them the simplest level of truth - that you are sick and going into hospital for a while. They don't need your confession of sins. It's probably not reasonable to expect your kids to understand and empathise. Get yourself sorted out and then get expert advice from the staff at the treatment facility on how to handle it with your kids. Personally, I don't see why they need to know the ins and outs of your addiction becasue tehy are far too young to understand or have any context for it. Most adults don't understand addiction.
I'm glad you are posting here and that you are able to get into the treatment facility. I think it's wise to detox under supervision rather than at home.