Open up x3_s3_palmount and add a variable check on the PC before they can summon it.
You just need to remember to zero out that variable before they can summon it again. Could do it when they rest. or you could put a timer on it if you wanted to.
@Kato_Yang, If there are no horses in your server, is disabling the horse menu feat necessary? I only ask because my module doesn't have conventional horses and I'm curious if I need to do this as well.
I handle them as an appearance only that happens when you blow different mount horns, there are no actual mountable horses to be found.