Is this your first child?
All children, in all aspects of their life - from being toddlers right through to being teenagers - need boundaries. By boundaries I mean understanding very clearly what behaviour is permissible and what behaviour is unacceptable. Then these boundaries have to be applied consistantly.
Children thrive with consistantly applied very tight boundaries. By tight I mean "black and white" thinking, without any grey areas. Like ABC are always allowed, XYZ are never allowed. As opposed to AB allowed YZ not, CX are sometimes allowed when circumstances are right (which are loose boundaries).
Having boundaries and working to set and maintain them is one of the central pillars to parenting. Children will constantly push the boundaries (to challenge and test if DEF is allowed, or if ABC are now flexible or not).
Back to your OP....
The only issue here is that you've not set boundaries. Your DD is struggling and suffering because of those lack of boundaries. It has never been established with her that bedtime involves (for example) 1 story, a kiss goodnight then she is expected to go to sleep on her own, in her bed.
It's not DD's fault that she cries for more stories, more time, mire whatever. Because on a primitive level she doesn't know what's expected of her. This has not been taught or established.
So it's time to make rules, set boundaries of what's acceptable and what isn't, and stick to it consistently.
If you have behaviour issues in otger aspects of her life, now would be a good time to tackle those too. Be it eating meals or getting dressed in the morning or whatever.
Children do, genuinely and without exception, prefer having boundaries. They are better for them. So it's not unfair to set them. Indeed, it is unfair on the child not to have boundaries of acceptable behaviour. If you don't get the child used to boundaries now, you'll have big, big problems in 10 years time when you have a teenager to deal with.