to get rachel its dependent on your first few interactions. I can tell you the exact things to say if you'd like or you can try to figure it out. I will tell you that you will know you can start a relationship with her by day 4/5 so you can restart if you aren't able to ask her out on a date.
So when you take your shower, go to her and knock. At dinner tell your mom you still have some adjusting to do. compliment your mom's dinner When you talk to her about Rachel's friend don't talk about her attitude stay quiet. If you did that when you eat with Rachel alone she will ask about relationships, say a few, then tell the truth, then question her. When you talk to her the next day agree she's cute. She will then ask when you're gonna take her out. Accept and you will start your relationship with her. I think that's what you have to do. Then just make the right choices to keep it