I was goin to say if she is scared of water and mud then its probly not the best idea to whip her. But if you went back to the place you got her from and they say she's been fine it must be confidence. You have to remember for all your horse knows that mud or water you want her to go through is a bottom pit therefore you both (horse and rider) need confidence and trust.
She's a mare she bound to be stubborn at some point
My friend just bought a new horse and she can't make him canter behind other horses or next to them but everyone else that we ride with can so its a confidence issuse for her.
Just keep working at it
getting more and more confident. If you or your horse tenses up around the mud/water you could just take her for a walk on your own and talking to her and stuff, and then when your relaxed take her back to the mud/water.
Probly the advice I just put isnt the best. Just an idea :L
Good luck x