Oh, what a great idea! A new life to watch, something happy to see everyday, and talk about with visitors!
I would suggest a foster kitten that has been in a home, rather than a shelter kitten, to ensure a friendly cat. Also, if the kitten is about 3 months old, it will already have many shots, and be able to blend into a new home easier than an 8 week old baby.
And discuss the kitten care, as far as who keeps the kitten long term. You may find that your Dad wants to keep the kitty. I just think this precious kitten is going to be wanted by everyone. So you don't want hurt feelings. Maybe plan to give Dad first choice to keep the kitten if he wants to, then your sister, since your Mom wants her to have it. Then you won't get your heart broken by thinking you get to keep the baby, and it goes to someone else.
I'm sorry about your Mom. She is lucky to have you. And as strange as it sounds, enjoy this special time with her. My Mom died of a brain tumor in 2002, and there are many happy memories that came from the sad time during her illness.