Miracleseeker, so very glad to know the Benadryl worked for your mom, that's the best news I've heard in quite awhile! And so happy that she has partial dentures and improved ability to chew, it should help immensely in providing good meals for her.
It does happen sometimes that a person eats plenty of food, seemingly, but yet does not gain weight. I doubt the coconut oil has anything to do with that. I would continue what you're doing, maybe make smoothies with the coconut oil, peanut butter, and chocolate syrup (it seems to me she liked all three of those) with milk or soy milk if she doesn't tolerate cow's milk. You should be able to make one, divide it up into portions, freeze it, and then thaw out a portion for an in-between meal snack. You could also add malted milk powder for extra calories.
As I wrote earlier, I would not expect very fast effects, if at all, from coconut oil. There just isn't enough research to even know whether it is effective for folks with PD. Plus there are different kinds of dementia, and if it is in fact effective for Alzheimer's, it still could be that she experiences a different form. At any rate, despite what apparently worked for Mr. Newport, he was younger, and perhaps less advanced, and that alone could make a difference. I would just continue, increasing the amount if she tolerates it, and give it a few months for a fair trial.
Regarding constipation, Benefiber is often helpful, because you can stir it into mashed potato, baked beans, as well as beverages, for extra fiber. Otherwise, has her doctor suggested Miralax for her? This is designed to help people with slowed peristalsis of the colon, as happens with PD.
You are doing a fantastic job of caregiving, as always, and deserve a medal. I wish I could help more, I certainly would if I could.