I agree, this needs to end before something happens that ruins you financially, or legally. The parents dump their kid on you, what happens when she gets injured, or you have a personal emergency and have to leave home, and kid is left alone by parents at your place? I know OP doesn’t want to hurt a kid, but the parents already gave the horse they owned away. Either stop the kid coming over, no matter how sorry you feel for her, even if that means giving the horse back to the parents, or demand one of the parents stay there the entire time. My guess is the parents will refuse to stay around, and will demand the horse back. Give the horse back, it’s not worth a court case. . They weren’t making a gift to OP, they were hiring a nanny for a kid they don’t have time for. OP can’t fix the situation, just be a nanny and have tons of legal liability.
I wouldn’t be surprised to have the kid have another meltdown if the horse visits to OP’s house end, and to have all kinds of accusations happen. Ending the situation is necessary, and it’s not OP’s fault that the parent broke their kid’s heart.
I bet the parents will never agree to stay with the kid, because they just want a babysitter, and won’t stay with their daughter. It may take giving the horse back to stop the problem. Don’t let your heart, and your compassion for the kid expose you to all kinds of danger. You can lose everything with one false allegation. I know of three people in my area who had false allegations against them, all three were exonerated, the accuser admitted they lied, and all three people lost their careers, and have many people who will never believe that they are innocent.