It's been my experience that if they are not sleeping, they are not getting tired enough to sleep. There are 2 kinds of tired. There is physical and mental. She needs some physical stimulation to make her tired. She needs a safe way to climb, walk, run, dance, and jump. At her age she is all about learning how to do these things and needs a safe way to do them. She's too short and little to play in the tunnels at McDonald's. So I suggest you get her a small individual size trampoline, lots of music, encourage dance time and some structure she can climb. You could get something like a small ball pit and or a slide she can climb safely in the house.
The other thing she needs is plenty of mental stimulation. She needs to have a large amount of books she can look at without being in too much trouble if she rips. So I suggest lots of chunky board books. But also, lots of books of all kinds from the thrift store. She needs to see and hear the written words all over the place. You can teach her out to pound play dough, pour rice from dish to dish, wash her toys in a small amount of water, smear shaving cream on the table with food coloring etc. This is an age for exploration and soaking up learning of all kinds like a sponge.
If she is getting both of these types of stimulation, a strict schedule or routine is not needed. My kids can and will lay down early, late, and sometimes not at all. But without a doubt, if I do lay them down, they fall asleep. At her age, she needs that nap and will become very disagreeable if she is not getting it. But she doesn't want to miss anything. So her mind and body needs to wind up enough to wind down after.
Try this with her baths. Since you have to stay in the bathroom every minute, this should be safe. Get some fizzy balls that are bath salts that are for making a person tired and relaxed. I am tired and the kind is not coming to mind. But look for calming scents. Put on some candles, play some soft music, and be sure to use only a very soft voice while you sit with her in the bathroom. Make sure you do this after a full day of all kinds of activities. See if she doesn't come out of the bathroom with a much different attitude. Also, keep all the lights low around the house with only night-lights and or soft colored lights. Mood is everything.
Suzi