Grandparents want to be home together, but my grandmother has been diagnosed with dementia. Any advice?

There are probably many places they can room together. If needed, they could maybe be in different rooms but spend all their non-sleeping time together.

It seems like from what you've said that they can not go home alone together. A disaster in the making.

I agree you need to try to keep them together. If they both medically qualify, Medicare pays in full for 20 days in a nursing home, then another 80 days at 50% so I would try to find a nursing home where they can occupy the same room. Work with the hospital SW to find a good NH that will accepts Medicaid, most will allow them to stay with Medicaid pending. Then see an elder law attorney to help you establish a miller trust so your grandparents qualify for Medicaid. Medicaid allows your grandparents' funds to pay for an attorney to help them qualify.

Can they go to assisted living together?

It sounds like living in a private home together is no longer safe. Can you tell them you will do everything you can to get them a place together and then make that the goal?

IF it's not possible for them to stay together know that this is not your fault. It is the reality of the situation. My only other piece of advice is what NOT to do and that is let them move in with you.