@acidreflux714,
What does your wife say? How does she want to handle it?
This has to come from both of you, as a united front. Your wife needs to make it clear to her daughter that, when she gave the kindle to you, that she actually gave it away, and it no longer belongs to her. That means that
permission needs to be granted if she is going to borrow it, just as surely as if she were older and borrowing your car.
She doesn't get a free pass on permission and ownership boundaries just because she used to own this particular piece of equipment, or she doesn't fully accept you, or whatever other excuse there might be.
She gave you something. It's yours. It's no longer hers. That means that she can't just take it whenever she feels like it.
I suggest you change your password anyway, more because then you can fully use the piece (e. g. if you want to read something that isn't appropriate for tweens), than as any sort of vindictive measure. You are entitled to have full ownership of it and not some maybe, sorta, kinda but you let her play games and this, that, and the other thing.
No. You don't. You allow her to play games on it if you sign in for her, to your piece of equipment because it is
your property.
I think ownership boundaries are blurry here, and I think that by just letting her use it whenever, you've done some of the blurring. If you want her to respect this as being your property, you are going to have to draw some sharper, clearer lines here.
But get your wife on board with everything, and present a united front. If your stepdaughter thinks that she can divide and conquer the two of you now, it'll be hell when she starts seriously dating, learning to drive, etc.