Living with an emotionally immature parent

I'm 19, and the oldest of two, it's just my sister, mom, and I. My father has a rare form of dementia and my childhood was pretty ugly because of it. We didn't spend much time at home and when we did it wasn't for long. I know my mom has trauma from the experience, as do I and my sister, but she copes with it so poorly. She uses it as an excuse and to shirk of responsibility to me or my younger sister. I am by no means a freeloader, I assist with my dads care, have two jobs, am a full time college student, do my best to clean the house, and pay for my car insurance, gas, and pretty much anything I need or want. She still always wants me to do more, it never ends. I entered a serious relationship two months ago and it has devastated and disrupted my moms life. During finals week my partner and I were not home often, and ate out quite a bit, this led to my mom deciding not to cook anymore. The past month it has been fend for yourself, which is fine for me, but less fine for my highschool aged sister.

She nags constantly and has sort of ridiculous double standards. Tonight my partner and I decided to go out for dinner and while I was getting ready I noticed a plate on her lap desk underneath her tablet. Some background, she will scream and pitch a fit if anyone leaves dishes in the living room. So I sarcastically called through the house, 'whose plate is this' and when she said it wasn't hers I asked why she would put her tablet on it instead of taking the ten steps to the kitchen so no one would knock it over even though it's not hers. When she told me to do it I pointed out the double standard, and she flat out said "that doesn't go both ways, you do what I ask of you" She said this in front of my partner who was shocked and horrified at her rudeness.

She's also incredibly bad at cleaning in general, she cannot for the life of her seem to maintain cleanliness. My partner and I cleaned off several cluttered areas in the house and within 3 days they were covered in shit again. My mom has these ideas and plans and has started repainting large areas of the home, while it is actively a mess. I don't like to say this, but it is basically a hoarder situation and I am at my wits end. I plan on moving for university in about 14 months, but I'm scared that if I leave the house will fall apart and my sister will be burdened with my responsibilities. I've tried gentle parenting her, being more forward, even involving 3rd parties because my opinion clearly doesn't matter, nothing works. How can I at least try to set up my sister and mom to be able to maintain the home when I am gone?