A vapor barrier might be helpful if the stalls floor level is higher than the ground outside the barn. Water seeks a level, so if stalls and outside ground are the same height, a vapor barrier probably won’t help much unless you do additional things with drainage outside.
Gutters with downspouts directing water into pipe leading away from the barn, french drains around the barn, leading rain/snow water away from the barn. Nothing will be cheap, though with a good plan, you may be able to do it yourself.
Best to get a barn builder, drainage expert in, let them assess your ground issues to find a solution, then make a plan to deal with it.
My BIL the builder, adevised us to bring in a LOT of sand base before building our new barn. Raise the base by more than we ever would have thought. But he was the expert! We were SO lucky to have him directing things! We bought a truck load of sand every time we got a few dollars ahead, for a year! Then we had a guy come in, push all the sand into a big base before winter. Sand settled, was quite solid by spring to build the barn on. But the quantity! We raised the barn more than 4ft from surrounding field dirt. I bless BIL on a regular basis because the barn has never flooded or had wet stalls over a lot of years. Despite torrents of rain, water racing across the lower barnyard in front, water has never gotten close to the barn doors. Water all leaves pretty fast, we are above the river with good dug drains I keep mowed and clean, but water is still a force to be reckoned with! 6 inches deep can knock you down!
We have added a lot of socked, perforated drain pipe (tile) to aid water drainage and it really does help lead water away faster. The “sock” is a fabric cover to help keep sand and stones out of the pipe. But getting drain people in will let you see things more clearly, they will tell you why you are having issues with water. Then what solutions will help you best for the money. You might need to do things in steps as your budget allows. We had to. Professionals in to replace old, broken ceramic drain tile crossing two of the fields. That made an immediate difference on wet fields and flooding! Water left much faster. Now that we have a backhoe, dirt cutting tool to make pipe trenches using the tractor, things are easier to get done.