It must be tough to witness your dad's suffering at the same time that you are still grieving the loss of your mother. It's a lot to manage.
It sounds as if your mom, in caring for your dad, was an emotional anchor for him. Now that his anchor is gone, it really is like he's a ship adrift in a vast ocean. The assisted living facility is by no means a familiar harbor to your dad, though he is probably in good, safe hands. As a result, it seems fairly normal that this results in your dad being confused, and crying often, especially if his aging process has negatively impacted his cognitive function.
Even if one part of him took in the information that his wife died, another part of him may be struggling to process this information, or just doesn't want to believe it. It makes sense that he'd long for everything going back to the way it was before your mom became ill and died.
My guess is that you'll end up having to weigh the consequences of taking your dad back to the house, or not. He's only been at the facility a short time; the reality of his situation may settle into his consciousness the more time he spends at the assisted living facility. If you were to take him home, and he were to, in your words, "start the process over," it might mean short term pain but over the long term, a better outcome.
On the other hand, being back home could ratchet up your dad's agitation or insistence about wanting to go back home to live.
Given that he is at an assisted living facility, you might want to ask for a consultation with those who are spending time with him regularly. You would benefit from someone giving you an assessment of your dad's cognitive functioning, and based on this, you might find you have the answer to your question all on your own.
If not, you could also ask the opinion of those caring for your dad about whether it is wise to take him to the house to confirm your mom's absence. If a psychological assessment has not yet been done, you could certainly ask for this at the facility. Your dad may also need pharmacological intervention to get through this confusing, sad transition in his life.