Re Horse #1, there is a partnership, here. Is there is no agreement on ending the partnership the a court would likely order the sale of the horse at auction. The proceeds would be divided based upon the facts as demonstrated.
Re Horse #2, the stable will likely have an agister's lien for services provided. The stable may perfect and forcloseon the lien IAW local law.
It would be in everyone's best interests to act like adults and resolve their disput(s).