Oh sweetie, I'm so sorry.
I know you feel guilty, but that conversation was needed and you're so brave for bringing the subject up, knowing how hard it will be for your family. My Grandad had Alzheimers so I know how hard it must be for you.
If you need to feel in control, then the diet doesn't have to be the most important thing to you - family first! Make sure you contact your mum's GP and her local council. Chances are you can get your dad some help, both monetary and respite if she gets worse.
I'm so sorry this has happened to you, you must be going through the emotional wringer! We're all here if you need to sound off or just clear you head - as you say, get things off your chest.
Take care honey, I'm thinking of you. X