How long would it take to complete the process of putting my Mother in-law into community care?

Maybe get her declared non compes mentis in a court of law with yourself as her guardian. After that, have the evaluation made and have her place accordingly. My sister had her husband placed in care due to early onset Alzheimer's, as she could no longer move him around. He maintained his good looks, but would fall on her. He remained four years, at her expense until he passed. She checked many facilities, and found this very special one near her home. She visited him daily to pick up his laundry and make her presence known. So, if you are involved in placement, make the decisions, visit her, I think you can do it with a clear conscience. She didn't transition him from one place to the other. It was home, and then, finally, she couldn't manage for fear of her safety. The only barrier in time would be if there is room for her; and generally, the turnover is fairly steady.