My stepmother has been diagnosed in the early stages of Alzheimer disease. Although we got along well for many years,about 6 months ago she began making irratonal accusations against me. For example has accused me of coming into the house when they are gone (a three hour drive each way ) and stealing knick knacks. She has accused me of taking my Dad's military souvinirs, when he gave them to me years ago. she accused me yesterday of trying to "sell the house out from under" her and my dad. How do I deal with this kind of thing? I could ignore it, or I could try to reason with her. For example, I could point out that I couldn't sell the house even if wanted to and would gain no benefit from leaving them homeless. My dad is in denial about the whole thing, so he is not much help.
Your question brought back memories of my now deceased wife. A few years after being diagnosed with AD she went through similar stages of "paranoia" In her case she accused her mother (who was still alive at the time) and her sister, of coming to our home and stealing her jewelry. Like you, they didn't live nearby and they also hadn't visited us for quite a while. As you seem to be learning, it is fruitless to explain to your mother-in-law that you didn't take those things. Her accusations obviously shouldn't be taken seriously and you need to remind yourself and others that the Disease is causing her to act this way. Unfortunately this behavior will probably continue until her cognition deteriorates to the point that she no longer can make the accusations.
I recall that my children and I used to laugh about Mom's "stolen jewelry"; not in front of her, of course. This helped alleviate any tension that the accusations might have caused. I would also suggest that you speak with you Dad about the fact that your mother-in-law may benefit from medication that might alleviate this and other behavioral type issues that your mother-in-law may be exhibiting. Suggest that he bring it up during the next doctor's visit.
I would also suggest that you try to find an AD support group that meets near where your Dad lives and encourage him to attend some meetings. If possible, even go with him. By attending he will realize that others are going through the same thing as he is and the discussions will that go on will help him come to grip with his wife's issues.