Too often when a child goes through trauma, we start using it as an excuse for their behavior. We make allowances for the guilt we feel in an effort to make it up to them. There are two problems with that thinking. The first problem is that you can't make it up to someone that they were molested/raped. The second problem is that you are doing more damage by not making her take responsibility for herself. Right now your daughter does not respect you because you are not acting like a mom. Being dammed if you do, dammed if you don't means you might as well do what is right since you are catching hell either way. What does that mean?
You have to shift the control in your home. To do this, you must be calm, matter of fact (direct) and stick to your rules. The first thing is that your daughter is an adult so you need to treat her like one. She has a time limit for getting a job. You set that limit and stick to it (I usually say 60 days). Next, there are chores in your home. You are not a doormat. She needs to take on half the responsibility for cooking and cleaning. These are not going to be "fun" conversations. No matter how mad she gets, do not get emotional. Tell her you expect her to act like an adult. If she needs a counselor, then get her counseling but, she still needs to start contributing. Once she has a job she gets to pay rent, teach her to save up for her own place. If she refuses to do these things that is fine, cut her off. no money, no phone, no insurance. If she continues to do nothing after that, give her 30 days to leave and serve her with a notice. She still might not take you seriously. Two weeks before she is supposed to go, bring home boxes and start packing her stuff. She needs to see you are serious. Do not cry in front of her, do not yell, be calm. You need to remember that the time for being emotional is over. It is time to be a mom.