First, let me say I commend you for being there for your dad. I have worked with Alzheimers/Dementia patients for over 20 years. It can be very challenging. What works one day may not work the next day.
First, just to clarify, Dementia is really an umbrella term for any kind of progressive brain dysfunction, especially in the elderly. Alzheimers is a form of dementia.
Changes in his environment could absolutely be exasperating his symptoms. Its very common for changes to send someone in a spiral. Grief can also make it worse. Maybe visit dementia.com, or alz.org. They have great information and suggestions.
As for getting him to the doctor, thats a hard one. You know the family dynamics more than anyone. Its hard to say what would work. For close family members, guilt works good .(because they still love you). Maybe make him feel like he would be doing you a favor if he went. Key words are good too. Again, you would probably know what words get the best response. Maybe get a doctor first then ask him for suggestions on how to get your dad in there. Some doctors can be pretty sneaky.
And, you know, sometimes people really do lose the will to live after their spouse dies. My mother did. She died 3 months after my dad. Our family believes they had to be together.
I wish I had more help for you, it can be a very slippery slope.You don't want to make his problems worse. You're a good son. Good luck,and remember your friends at cann.com are here!!