M.,
You have already gotten good advice on the other posts, so let me just reiterate what they said & maybe add some things.
Each kid is very, very different. What works on some does not work on others, and what works on your child this week may not even work in six months!!
There is NO 'wrong' or 'right' way to do any of it. The important thing is to keep the child safe & secure & keep everyone as emotionally stable as you can in the long run. When you feel like you are getting overwhelmed take a deep breath for yourself & try to relax before you feel yourself getting overwhelmed.
Your daughter may benefit from a different nap schedule that what you have now, so that she is more ready for bed. You may even be keeping her up too late. My brother & his wife have been depriving my poor niece of sleep for years!! At 15 months your daughter needs at LEAST 12 hours of sleep in a 24 hour period, many people mistake kids getting that 'second wind' or 'slap happy' phase in the evening as meaning they are not ready for bed, when in fact, you have already missed the original window.
My daughter is 5, and we start the 'pre-bedtime' thing around 5pm!! She does not nap, so she is in bed at 7pm, and sleeps until 7 or 8 am. Around 5pm we start picking up our toys & things from the day & get the bedroom cleaned up. We talk about the day & what she liked or did not like. We shoot to eat around 6 or 6:30 so that she has time to digest the food before going to the potty, brushing teeth, washing hands & getting into bed for a (short) book. I keep an assortment of shorter, quiet bedtime books for her to choose from.
I think the most important thing is to establish a good transition period from busy daytime activities to evening, and especially a set routine for the transition & bedtime. Small children crave rituals & routines, it will help to signal to her busy, busy brain that the bedtime is coming & (hopefully) help her to get into a calm mode.
Kids soak up SO much information during the day, and we are all so very, very busy that I think sometimes we all put too much expectations on small kids to be able to process it all & shut off with almost no warning. I am not saying that is what you are doing, but they are simply NOT able to do that. They are still learning how to deal with emotions & excess energy so it is up to us to help them to shut this down & learn how to deal with it.
Most of all, they just need to know that someone they love is there, and they are safe. Sneaking out of the room is never a good idea, she'll wake up & get all upset all over again. Be patient with the process, but establishing a routine & sticking to it, especially at the same time will really help.
Good luck, and enjoy your daughter while she is little, they grow up WAY too fast!!
B.