C.R.
As a mom of ten, I would certainly say you are right, there is no power struggle, your little daughter is the boss, pure and simple. She calls all the shots. You are the servant running around behind her cleaning up after her.
The first thing I would do is take back the authority as a parent, and tell her she has to wear clothes. Period. Simply do not allow her to take her clothes off. I don't know what kind of discipline you use, personally, she would get a swat for taking her clothes off if she were mine. This would not be optional. Even if her shirt had to go on backwards so she couldn't unbutton it, she would wear clothes. That's what decent people do. You want to train her to be decent, right?
Then, decide whether you want to fight the potty training battle now, or wait until she is a bit older. Either way, she wears what you tell her to wear - be it panties or diapers or pull ups. Then, tell her you will not get her up at night or in public to go to the restroom unless she proves she can do it by going at home. If she has gone in her pants all day, then she may not get up at night to go the potty. Sorry. She has not earned the priviledge of using that excuse to get out of bed if she has not pottied in the potty chair all day.
You have a lot of very young children, I know exactly how that is. Sometimes your brain can get a little foggy and you don't see things as they really are. This little lady of yours is holding all the cards. Imagine, she is running around naked, making terrible messes on the floor, laughing and smiling at you while refusing to go to the potty, and you are allowing it. Not only allowing it, but cleaning up her messes. Be the parent. Stop this today. Take back the power. Again, maybe you should just forget potty training for a month or two while you reteach her and yourself who is the authority in your home. This is a God given authority, and you are supposed to be the one who makes decisions like this. She's only two, teach her NOW, or you will have a world of trouble in about ten years.