I have an autistic young adult and another who isn't diagnosed but most people assume he is. I just never ever let them be rude and hurtful to me. Ever. Not in childhood, not as teens. They don't get away with treating other people like dirt. As a result, they are extremely kind and loving and considerate for the most part. With some spectacular failings at times, every single one of which results in a very frank discussion with me.
I'd sit her down and say: I love you and it matters to me that you understand how to treat other people with respect and kindness, especially people who love and care for you. This is a life skill everyone must learn. You may not realise this but your behaviour towards your dad and me is rude and hurtful. You show no interest in us, you roll your eyes when we show interest in you. I don't treat you that way and never have. I don't ignore you, mock you or take you for granted because that is not how anyone should behave towards loved ones. While you are home I want to spend a bit of time with you, and not feel like a hotel concierge. I want to see you maturing into the kind of adult who appreciates and notices when loved ones make an effort for them. Some thanks for cooking, shopping, laundry, lifts to places, some interest in our lives - these are not big things to ask. They are so small and easy to perform, but they make a huge difference to us. And let's make a list of a few small things we could do together - a walk, swim or bike ride; a film, cooking dinner together, a night out or a day trip somewhere. I want you to do this with warmth and love and good humour.
Not one big lecture like this, but cover all those things in a conversation and make sure she has taken them on board. If she remains sulky I would stop doing anything for her for a few days - no lifts, no dinner, no clean bedding. If she leaves pans dirty, leave yours dirty so she has to clean them before she cooks. Don't greet her when she gets back from work, don't help her wake or get out of the house on time in the morning, don't ask about her day or call her down to dinner. Not as a war or battle of wills, but for a couple of days to show her what it is like to be on the receiving end of indifference. Tell her afterwards you hated doing it and it felt unnatural but she needs to understand what it feels like to be treated by a loved one the way she has been treating you.
Intelligent autistic people are perfectly capable of showing respect, affection and appreciation. Rudeness is not an in-built given trait of autism. I know loads and loads of really polite, warm, lovely autistic people. And lots of rude entitled neurotypical ones.