Have you tried not trying to get her to sleep? Or the naughty thing of letting her fall asleep downstairs in front of the telly?
Reason I ask is this;
My DD was a terrible sleeper at times. When she was about your DDs age we were struggling. They are half way between communicating and understanding and not.
So, I used to bath DD get her all ready for bed by about 7. We then let her stay up with us, but it was pretty much quiet time, but put no pressure on her to sleep. We would potter about, DD would have a couple of quiet toys out, and every now and again when she looked tired we were offer for her to come and have a cuddle on the sofa. Sometimes it would be quite late, and I was lucky and diddnt have to go to work, but DD gradually started dozing off whilst cuddling on the sofa. The biggest thing is NO pressure. If she wants to get down and carry on playing, let her. Once she had fell asleep and was fast asleep we would carry her to her room. Sometimes DP would go to bed and I would stay up, sometimes on weekends he would stay up.
What we decided is they we needed to take all the STRESS out of going to bed. Eventually she was falling asleep by around 9.30.
We did end up doing a cross between gradual retreat, CC and CIO when she was around 20 months, to get her to fall asleep in her cot, but we felt she had a much better understanding by then, plus she no longer associated going to sleep with something horrid. And because of this it seemed to work very quickly (less than a week).
Nothing else has worked so far, so maybe just buy taking all the stress out, letting her figure her own sleep pattern, and learn that falling asleep whilst having a cuddle in a dark warm room, with the tv quietly on, it may just help you.
The key is don't force it. It needs to be nice for here.
DD is now a wonderful sleeper, asks to go to bed, and although she doesn't often nap any more, some afternoons she curls up on the sofa in front of a Disney film and says "mummy sleep now" and off she goes.
And I really think it's because she learnt that drifting off can be pleasant and not a battle ground.
Like I said, you may have to correct things later, but she will be able to communicate by then and understand it. And in the mean time we wernt arguing over it, and I started to enjoy her more.
Not fiemr everyone, but may be worth a try
Good luck!