Dear K.,
It has been my experience that a 'fit', as I call them, that gets attention, escalates. Here is a suggestion that has worked for us. First, trying to reason with, argue with or otherwise deal with a child in the middle of a 'fit', just wears you out. They are not hearing you, and a 3 yr old, does not have the power to reason with you. You say that you drain the tub, and the other child gets out as asked. Here is what you might try...give your attention to the child that is obeying. Give praise and attention to the one who is listening and getting out. Ignore the fit. (naturally, be aware and make sure that she does not get hurt), and if there is a way to walk away, and still be mindful of her safety, do it. Once she realizes that her 'fit' is not affecting you, and that the OTHER child is getting your attention, I suspect that these 'fits' will subside. It may take several episodes for her to get the message, but let her calm herself... it may take a while, but do not give her your attention until she is calmed. Once she realizes that the fits do not get your attention, they will decrease in severity and length. This works in many scenarios... as long as YOU can maintain not giving in. Once you do, the child in control of the situation and they know it. If she is in an empty tub, there is not danger of drowning, just let her lay in the tub until she is calmed down. If you're in there to trying to talk her out, take her out or threaten consequences...she'll get tired and settle down. My guess is that after a few minutes of 'alone time' --- (again, make sure that she is safe/maybe stay where you can keep an eye on the situation, but she can't see you)--- I'll bet you'll hear the call for "Mommy... Mommy...." At that point, attend her call, ask if she's ready to get out now, and if the answer is "yes", commend her, and take her out for a little cuddling. If the answer is "no", walk away again, until she is ready to get out. Sitting by the tub, waiting for her to make a decision just puts her back in control and gives her your undivided attention. Maintain these actions at each bathtime, until she is willing to get out when told. Remember, you're in charge, Mom.
In my experience, 3's are worse than 2's.... and fits become a way of life for them---if they get attention & results. Mom, I'm in your corner!!!! I think this will make a difference in just a few days.
Don't coax her out with rewards....she'll figure out that "If I throw a fit, Mom will give me a reward to just get out...I can manipulate this to get candy, or toys etc..." She needs to understand that it's time to get out, just because Mom said so.
Good Luck....
S