There's no legal reason you can't do whatever you want.
There's also no legal reason for your mom and sister to let you keep living there.
The worst-case scenario is that your mother kicks you out of the house. Which, in my opinion, wouldn't be a bad thing for you if they do this because they're upset you went on a date.
You only live once
All sentient beings have photographic memories and, through DNA, they can store and recall all of their previous ancestors' memories. All the way back to their oldest sentient ancestor.