I would push for cooking with saturated fats since it's easy to just throw a glob into the pan. Meats and veggies will be coated without it being mentally and visually agonizing when they eat. I'm in the same boat with my parents and it is hard, but I was able to convince them to use lard and coconut oil instead of vegetable oil. If they're not adverse to butter, then get them to try that. Every little bit of fat counts.
Coconut oil in tea/coffee.
Appeal to your mom's vanity and say coconut oil will improve her skin? Tried it on mine and that worked a bit.
Without the fat to satiate them, your 'rents will feel the hunger more.