At 3 years of age, she's just a baby. No matter that somebody has been foolish enough to put a young child in the saddle on her or stand on his head on her back (!!!), she's a baby in a strange place (they can adapt to a new place for even a year or so!).
So, regarding bathing, I'd treat her as completely green. How does she react to a slow, sprinkling flow in front of her? On a leg? On front legs? On shoulder? Take small steps, be patient. You don't have to "assert leadership" if you understand it as dominance, but you need to make her comfortable and trusting with what you're doing.
She's probably not stubborn, just genuinely unsure, tense and, as such, testing her surroundings. Show her the rules, but be calm and trustworthy about it. Praise her for tolerating water on her hoof, then on her knees, then higher yet (when she truly reacts to that calmly), ignore her doubts and use approach-retreat techniques to explain it to her. When she shows acceptance - stops even for a second, relaxes, chews, exhales, blinks - take the water away, when she resists - let her move, but let the water follow her as well. As she gets progressively more accepting, you can introduce more elements of a proper bath.
Most of all, don't expect anything of her. She doesn't have to apply to any standards or rules, she's just a horse and she's honestly showing you how she feels - in this case, stressed about water.
As you admit you're inexperienced, I'd really, really suggest you to get at least a couple of lessons in groundwork from a reputable trainer. Nothing compares to a good hands-on assistance, eyes from the ground to help with your timing - you name it! It will benefit both your horses and yourself. And, quite possible, your husband as well.