Dad is ambulatory and Mom had a stroke in 2013 and is in a wheelchair. Where can they go, remain together, in a facility of some kind?

I would check for continuing care facilities. They have Independent Living, Assisted living, skilled care and memory care, a lot also have rehabilitation aka skilled nursing facility, nursing homes.

This will give them the best chance of remaining together as the facility handles all level of care. Obviously you are charged based on room and board, then they charge extra depending on the level of care required.

Ones that I toured keep their clients in the same room except for the Independent living and memory care, the rest just increased how much assistance they received in their home. Which were lovely, large studio apartments with nice bathrooms and little kitchenettes.

I hope you find the perfect fit, that will allow your parents to remain together for the rest of their lives.

Assisted living homes ,are always a good option ....

Does your dad have all/most of his mental faculties? Depending on how much care your mom needs, they may be allowed to share a room in ALF. It's really up to the facility to assess them. I think they'd want to keep them together if possible.

Do you know what your parents' financial situation is? AL can cost several thousands per month. Medicaid would be an option if their means are slight, and it pays for a shared room in any facility, which is more like a hospital room than an apt or hotel room. In-home care can work for a while but eventually surpasses the cost of a facility, especially with the amount of care your mom may require.

Do your parents (or at least your Dad) have all their legal ducks in a row? Durable PoA, HIPAA release, Medical Directive, wills? It's very important that they get this taken care of right away. May you find an awesome place for them!