Oesdog Major hugs to you!!!
I have read the posts in the past about your sons. I think your deciding to transferring their care to this facility is the best thing for you, your family and your sons. I think it would be a good thing if both boys could go together and start this new adventure in their lives. It might help them both to feel like they have each other.
I know it will be hard for you and there will be many days that you will think you have done the wrong thing. But they will need care all their lives and if you can be there for them at this point, you can help them transition in to their adulthoods. Your health and your husbands have been greatly affected by the stress/work of caring for them and I truly think that the best thing that can happen is you can learn to enjoy them as adult children in a new way with out the actual work of their daily physical care.
more hugs!