When a child has night terrors they don't wake up. Nothing is actually 'scaring' them, it's like their brain can't shut off. They have no memory the next day and would never 'play' or interact during or after a night terror.
I agree with the other moms who said that you should get her checked out for ear infections etc.
At 9 months she may very well have figured out how to get mommy all to herself in the middle of the night!!!!! Try NOT to play with her in the middle of the night. It will only encourage her.
I did not do CIO - but I think 9 mo is around when they say you can start sleep training, so now may be when you have to start a consistent routine with your daughter when she wakes up in the middle of the night. You and her dad should talk and agree on what technique you will use. Decide what your boundaries are and then stick with that EVERY night. It's hard, but consistency is the key.