I am so sorry that you have had to deal with this kind of trauma, its hard enough dealing with infidelity but even worse when your partner chooses to leave. It sounds like he is making some poor choices and in the end it is going to effect his life as well as the children if he continues.
With that being said, you have the right to ask him to sit down and talk. It sounds like he is avoiding you out of fear because he knows what he has done was wrong and has hurt not only you but the children as well.
I would recommend the next time he stops by to ask him if he can make time in a few days to talk. Let him know you do not wish to argue, but there are some matters that need to be addressed and it needs to be done soon.
Ensure the children are not at home when you set this up, when he comes over have him sit down and let him know that you are worried about him. Explain to him how you feel about everything that has happened and that while you respect his choices to leave the home you can not condone his choices of using alcohol and drugs. Explain to him that you are concerned about his health.........and while these are his choices you also must both consider the children's needs and mental health. Let him know that this is not good for the children and how all this is effecting them.
Ten weeks is long enough that its time to decide where to go from here. Some decisions need to be made if they have not already been started. I do not know what your situation is but it may be time to start the process of a legal separation to protect you and the children from any bad choices he or his mistress may make that could effect your life or finances. At the end of the day, he is making choices that could have a negative impact on you and the kids. Drugs are against the law and as such should he get caught there could be financial loss to your assets. Not to mention the fact that should he accidental harm someone (Drinking and driving etc) as his legal wife both of you have a lot to lose in a civil suit. By starting the separation process you are protecting yourself and the children.
I know this is a lot to take in right now with all the pain you are likely going though, it sounds like he has allowed himself to be sucked into this womens world and allowing himself to make choices which will ultimately harm himself. All you can do at this point is protect your children and yourself and try to explain to him that you are worried about him. You can not stop him from ruining his life.........but you can try to let him know you are concerned while protecting you and the kids.