He has a personality disorder. My Dad is paranoid, suspicious and delusional. He refuses to call a Plummer to fix the bathroom tub so we can shower; he thinks he can fix the ceiling under the leaky tub by painting it; he refuses to fix the ceiling light in his bedroom. He gave the home to a Grandson and promised to keep the house up but now refuses to do so. We are expecting a snow storm and he has on the heat and the air conditioning. I can't leave because my Mother has Alzheimer's. He guards her and the have no quality of life.
How do I know? I tried it and was left on my lonesome with Mum after all the helpers pulled out!
Does he see his Dr. for anything? A Dr. can do a very (VERY) basic evaluation but you'd probably have to get dad there under false pretenses. Does he have some medical issue you can use as an excuse to get him to the Dr.?
And if this Dr. determines that there is dementia then what? That won't change your dad. It won't improve your parents' quality of life. He won't stop being paranoid, suspicious, or delusional.
When there is Alzheimer's and/or dementia like in the case with your parents there rarely is quality of life. Dementia and Alzheimer's rob the person of quality of life. It's very sad. I'm so sorry that you have to watch your parents decline like this.
It doesn't sound as if your dad is capable of caring for your mom. Do you have siblings? If so, have you all gotten together to discuss this? Your parents can't continue to live on their own without disaster striking. And you're spot on about getting your dad to the Dr. Use any little excuse. You have a question about his medication or you're concerned about a bruise he has on his arm. Anything.
Good luck.