Hi P.,
What is your 15-month-old's behavior at 2am? Nightmares are possible. Does she watch any movies/television in the last couple of hours before she goes to bed? Have any new foods been introduced? It could be stomach aches/gas. Does she eat anything in the last couple of hours before she goes to sleep?
I would call the pedicatrician for a check-up. Tell them what's going on, and see if they can find any medical reason behind it. If not, your 15-month-old just has to learn to stay in bed and go back to sleep on her own. I know that's probably not what you want to hear, since that will take a lot of effort on your part. You can also ask your pediatrician if reducing or removing the midday nap might improve her night time sleep.
At about the same age, my daughter had trouble sleeping at night. She was taking a midday nap that lasted about the same as your daughter's. My daughter didn't have trouble sleeping as long as someone was holding her, which meant she was in an upright position. The pediatrician thought she had acid reflux. She spent a few months taking zantac with no improvement. I discontinued the medication--still no change. I finally started to cut out her naps, and she started sleeping better through the night.
I hope I've helped.
-J.