Me too...
Back when Dad was about 59 (he's now 64) we had virtually the same experience, except we were not given an option of paying for additional care (an understandable amount when you think of the cost per hour of hiring someone to do the job, but an impossible amount for any normal person to be able to afford). Like what has happened to your Dad, my mother got a phone call from the place my Dad was staying at to give her some respite, and they told her she has to come pick him up because they couldn't manage him. Like you, we were astounded because if they couldn't cope with him, trained carers and multiple carers, how ever did they expect my mother to be able to come pick him up and care for him by herself???
At the time, my mother was absolutely cared out and this was the straw that promised to break the camel's back. What you are going through now, is very very tough. At the time, the whole situation seemed so ridiculous to me, I started having ridiculous thoughts of my own...what if I were to swaddle Dad in blankets and dump him on a church door step over night, would somebody care for him then? What if I could manage to frame my Dad for a crime, so that they would put him in prison...at least then he could have the state look after him....Yes, yes I was just being silly, but the situation was so unbelievable!!!
But don't panic yet...I live in Australia, so can't advise who to go to in your country...but I am guessing perhaps social services, or any institution that assists carers where you are...you need to go speak to these people and find out what the true options are. As we found out, it just depends on the home. Some homes can manage people like our parents and some can't. We ended up finding a nearby home, that seemed no different to the other home, but they were prepared to look after someone like Dad with the same number of carers. Hopefully if you can get some advice from someone like social services they will be able to tell you whether there is a suitable home in your area, that provides what they call here in Australa 'high care'.
Best of luck to you, my heart goes out to you and your family,