E.C.
Make it totally boring when she wakes up in the middle of the night. Keep lights to a minimum, don't talk more than you have to, don't play games or give lots of hugs and kisses (a little's okay, for calming). Tell her it's nighttime and time to sleep. Check on her when she cries, make sure she's okay, then turn out the lights and leave her alone. Then don't go back right away if she cries again. Not too long, just a tiny bit longer than you would otherwise. So if you want to rush in as soon as she cries, wait just a minute. Then go in and check and leave again. Also, you say you have a 2 month old. Did this night waking for your daughter start when you brought the baby home? Does the baby wake at 3am? Try explaining to your daughter that the baby needs to be fed in the night, but she's a big girl and doesn't need feeding at night. I hope some of this helps.