stubborn mare? or scared rider?

kicking and beating the horse won't make her less afraid or any more willing to do what you want.
Start small, work on just leading her around the barn and arena and asking her to stop, and start, and turn calmly. Then lead her through a puddle or by obstacles till she obeys you quietly.
the KEY is for you to be the leader, the one she trusts. Don't loose your temper or yell, just be patient and keep asking. As soon as she even starts to to the right thing, praise her and release the pressure.
Do the same things while you are in the saddle. Keep your cool. My mare used to refuse to go forward, but she was perfect if I led her; anytime she would balk, I would just get off, lead her a little way, then get on again as if nothing had happened. She gave up the balking habit quickly. No fighting, no yelling, no whipping (tried that, didn't work.)

For water crossing, you may have to lead her across quite a few times, or have her follow another horse that she trusts. Don't loose your patience, you'll make the problem worse and longer to resolve.
Read John Lyons, he has exercises you can do to correct this problem.

I agree with the above reply. Lots of ground work to build her trust with you, you will have a good partnership once she learns that you will keep her safe. Always keep your composure, and if you find yourself getting really impatient or frustrated, take a break and collect yourself.
When I started training Walka, we have alot of water on the trails here, so I knew we had to make his first crossing very positive. I have a friend on a very calm horse lead and cross first. Walka wasn't too sure so we stayed on the other side of the creek and just waited. I kept him pointed where I wanted him to cross, and just waited. I would give him a cue to move forward, not kicking, and even if he shifted but stayed looking forward, I released. Remember the real goal isn't to cross, but to cross with your horse calm. Takes time, but with each new crossing, they look to you and trust you to keep them safe. Happy to say that first crossing took about 20 -25 mins to accomplish calmly and all the other crossings he encountered he never skipped a beat. Good luck!

Perhaps in the past she has had a bad experience with mudholes. Violence never solves anything. I hope you get through with her...goodluck...