I didn't check the rules (oops!)
I made the second one as a way to separate my English and Western horses. I also wanted a small place for the Western horses instead of just being all over the place. Both facilities are in the same game/save and are literally right next to each other.
I was over at ????Equisim Alliance???? and saw that they had multiple stables for each member. That's what I needed to do so I did it to make the game easier.