In my experience with my soon to be 15 month old who is all of the sudden having trouble sleeping as well, I have had to extend his A time A LOT and it is a huge adjustment.
It looks like from your schedule that she is only up for an hour and a half in the morning before she goes down for a nap? I think you should try extending out that A time. This would adjust the day as far as A times go in between both naps. In the afternoon after her second nap you have her up for 5 hours! That's a big amount of A time compared to the morning. So, I would try maybe going for 3 hours of A time at first and then continue working till you can get 4 hours of A time. We have had t begin doing this with DS as he is beginning to get ready for the 2-1 nap transition. I think extending the A time really helps prepare them for that!
Also as far as her waking as soon as you walk out of the room....I would suggest WIWO. If you're not too familiar with WIWO (as it took DH and I some time to get it down), go in to reassure her that you are still there but reinforce that it is bed time. Then walk out when she calms down (we don't touch DS either as it seems to work him up too much). I have a post on this thread (Sarah/Anyone PLEASE HELP!) with some good advice that was given to me with WIWO. If you continue staying in the room till she's asleep, she wont learn how to fully put herself tosleep without you.
One more point, have you thought about moving her to her own room? This might help with her going to sleep with little distractions
HTH