This is my first time doing anything like this.
Me, too. I was desperate. Most of us usually are by the time we arrive here.
my son has his daughter 4-5 days a week even befor he lost his job, now he just spends more time with her instead of me watching her.
The fact that your son takes responsibility to care for his child is major in my view. It is also a hopeful sign.
As I stated, it is my belief and experience that you cannot motivate somebody else. If you decide that you want to let your son and grandchild live with you, realistically, you need to let go of any expectations that he will change in the ways you want. That is up to him, when, how, and how much he wants.
If you decide that he can stay, it is recommended that you set a time limit. You can then reassess after that interval. You also need to think about conditions, limits and boundaries to make the situation clear cut and more comfortable for all.
Are there responsibilities that he can take on to help you? Yard, house, other?
Can the house be divided where he has his own space, and you have your own?
What expectations do you have of him? Are they realistic? Are these goals he has for himself? Does he have any other housing alternatives that might be better for him?
Living with people his age, or another adult, where he would not be dependent on his parent? Is Job Corps a possibility? They do accept people with mental illness.
Is he receiving welfare (AFDC/Aid for dependent Children)for the care of his child? If he is, sooner or later they will have the expectation that he look for work, or apply for Job Training, College, the Department of Rehabilitation or SSI, if it is determined he cannot work.
That way the expectation and mandate that he be productive will not come from you. It will come from this other agency.
If he is not receiving AFDC I suggest he apply to defray the expenses that fall on you. I would also make a condition that he contribute the bulk of the payment to you to cover food and household costs, leaving just a very small amount for spending money. You should not support him and his child, while he receives financial benefit. That is wrong and it is risky.
When he sees you getting the bulk of the payment, that may be a motivator itself. He might seek to establish a separate household in order to control the payment himself. That would be good for him, I think.
I would confront directly in myself, and later with him, the fact that his child is his. As long as he is the legal and custodial parent, he is free to leave with his child whenever he wants. How will that be for you? To what extent is your willingness to have your son live with you motivated to have your grandchild with you? These are not accusations. They are important questions to ask yourself, so that you do not suffer down the road. Things made explicit are better than those that remain covert.
What does your son want to do with his life? I understand he does not want to go to group therapy, but there area all kinds of alternatives, including 12 step groups.
Is he doing anything socially or recreationally? Gym, biking, swimming, Church? Are there family activities he is involved in?
I do not ask for you to tell us. The questions and answers are for you and your son.
There needs to be an ongoing conversation happening, whether your son likes it or not, if you decide to open your home to him. If he does not want to openly talk through and plan, I would seriously think about whether you do this. Your life is impacted greatly as is his child's. This all needs to be tackled and negotiated directly, I think. For it to work and be a healthy situation for all. Especially for your son.
Take care.