I remember having the same issues when Jett was the same age. I honestly think it is an age related phase.

Jett slept through right from day one (well 6 hours anyway, which is huge for a nb!) and was great up until about 5 months. He then started waking up every hour or so. We managed to figure out this was all to do with the food/hungry thing - he needed solids. But the nightly wakes up just didn't settle after solids was introduced and there was a phase around the 7/8 month mark where he was waking up all the time. And then suddenly he just dropped it back to twice a night, and then once a night which he kept up until just after 12 months. I was exhausted at the time and trying everything to resettle. Lucklily he was really easy to settle, which I put down to us co-sleeping. We would offer a drink of water, put the dummy back in and then go to sleep in spoon position with our arms halding him securely. He usually didn't fight much after that.... until the next time he woke. And FWIW I don't think 9.30 is too late, Jett goes to bed around then too and has for a very long time. That is when he is naturally ready to sleep, so I don't try to change it. Perhaps, if you are able to, just follow her lead. Babies have natural rythyms and I found that every time I tried to tinker with Jett's things started to get out of control. But as soon as I relaxed and went with him again it all settled down.

My advice - Don't fight her on the sleeps. During the day if you notice the tired signs, put her down but if she is still not interested in sleeping get her back up for another 10-15 mins and do a quiet activity like reading a book - but away from her bed. Eventually, she will let herself go to sleep, especially if she thinks you aren't forcing her to, as I think this is when the power plays start. They want to feel in control of their life and they are testing that out in any way they can. They might fight you on the solids too for the same reason, one of the reasons why Baby-led Solids can be beneficial for strong-willed babies. And don't think of it as giving-in to her, think of it as picking your battles. If it isn't going to hurt her then at this age you won't do any long-term damage, or create a monster! Save the power-plays for the 'terrible-twos' when they really test the limits!!

And try to take care of yourself and share the re-settling responsibilities with your DP. It is exhausting but it will pass!

I hope that helps! Or at least gives you food-for thought to adapt it to your situation!