Alas I fear you have two choices:
- adopt Tiny Cat out (trying like hell to see that she ends up in a very loving home);
- exercise epic patience while a naturally-nocturnal feline slowly tries to learn to live like a diurnal ape.
It's really that simple, and I'm sorry to bear that bad news. Tiny Cat means you no harm. She only longs for you to share with her the sheer joy and excitement that, in her eyes, nighttime brings. Cats who learn to sleep at night have really done an amazing thing. And I don't know how old Tiny Cat is but if she's anywhere vaguely in the kitten or adolescent ballpark, that just makes it all the harder for her to learn this. As cats get older, they get "sleepier," and what they basically do is start sleeping/dozing most of the time both day and night.
And that's the reality of life with a cat. Some are better at adopting a day shift than others, but none are genetically programmed to live that way.
Please don't "hate" Tiny Cat (and I know you wouldn't). Just help you and her to make the best of the flawed situation, however you can.
... sad for you both.