I'm going to leave my older sister alone at home
Why do you think that's a good idea?
Because I'm a nice guy and I was alone at home and I called her and asked if she wanted to come and she said no.
That is good to respect her wishes. If would be good to check in on her if you were asked to watch her.
It's cool, I want to spend time with her and prove that I'm not nice just to get people to think I'm good.
It's really good that you love your sister and can respect her wishes. If you go out again it might be good to invite her again to keep her in the loop.