This question is in reference to a specific situation, but I'll phrase it more broadly. What is the effect of saying "no" to an invitation to sleepover her place?
Aside from the obvious consequence that I may have just turned down an opportunity to have sex.
Assume that she desires me to sleep over her place, because she's already emotionally invested in me.
I see two possible consequences here: 1) it makes her want me more (you want what you can't have) and/or 2) it creates resentment which stifles chances for future sexual advances.
which effect do you guys think is more likely?

This is imporant bc i need to switch up the power dynamic in a relationship, as I've been pussy whipped recently.

Her reaction could go either way; it depends on the girl and on the prior dynamics between the two of you; but if this is a girl you're already having sex with and you want to change the dynamics then by all means reject her invitation.

Yes prior sexual relationship w her.

I could F close if I tried hard enough, but she acts like she'd rather just cuddle and shit. I want to say no (and make it obvious that I'm seeing other girls) to DHV; but I don't want it to backfire by her getting the idea that we're NEVER going to have sleepovers anymore.

It could definitely backfire for sure and it's obviously your call but if it were me I'd take my chances and flake on her, particularly if the invite was for a weekend night - and then no matter what you do, do NOT be available for her texts or calls on the night the sleepover was supposed to occur. I don't know enough about the two of you and how much you value your relationship with her to make an informed recommendation here however.

I disagree with the advice to flake. WTF kind of pussy does that? Say what you mean, be the master of your domain. If you decide NOT to accept her invitation, do it with style. Just say you already have plans. And then I would definitely be unavailable to text, etc. IMHO, if she takes the rejection poorly and it's a problem, you just saved yourself from having to deal with an immature bitchy baby.

I was using the term flake loosely in expressing agreement with the OP's idea of "saying no to an invitation to sleepover". OP PM'd me and based on the further information provided, i responded that IMO he should definitely reject the invite.