My 2 year olds sleep is awful! She was sleeping through the night from 7pm-7am from about 10 months, at about 18 months she started not going to sleep till 9/10pm.
We finally managed to crack that a month ago but it's all gone to pot again. If she has a nap in the day she won't go to sleep till late (she's still awake now). If she doesn't have a nap in the day she's so tired and asleep by 6pm, then awake again at 10pm till stupid o clock in the morning!
Have you taught her a way to get back to sleep when she wakes up?
How does she go to sleep at bedtime? Does she have a sleep trigger?
That is the skills that she seems to be lacking. Babies/toddlers/children need to learn the fact that when they are tried they need to go to sleep, this isn't a skill that children are born with so they do need to learn it. Otherwise, as you have found, children will fight sleep.
I am not suggesting you leave your child to scream or anything like that, but it is likely to involve some (lots of) crying and frustration from your daughter.
A 2 year old needs 12-14 hours sleep in 24 hours so I would aim for a 7pm-6/7am night and a lunchtime nap of at least an hour at around 12.30pm.
You just need to bite the bullet and do it. I would find a time when you have support to cope with the lack of sleep. Make sure your DH is on-side with you so that you can share the load when one of you has had enough.
Then just sit by the cot and keep lying her down, "sleep time now, nan night" kind of thing. Repeat, repeat, repeat always being there, giving reassurance being calm (not shouty) but ultimately always remaining consistent all the time, every night, night after night.
She will get it if you stay consistent. You will probably find her behaviour massively improves generally once she is getting more sleep.