I feel like not going to give my mom more time to process my sister coming out.
Why won't you give her more time?
I'm waiting for her to deny it
It's good that you're being supportive of your sister, but you should also try to be patient with your mother. People from older generations can have trouble adapting to modern social norms. If you give her a little bit more time and talk to her a bit, I'm sure she'll come around.
She does not need more time, and she should accept my sister if she wants to.
She may need time though if she is really against your sister coming out. It's important to make sure she isn't too shocked by it.