You say you don't want to be in the middle, so don't be,
The issue is between the pony owner and the BO, It is the pony owners problem. She has done something alot of people are good at. She has made her problem yur problem. Don't play along,,
I wouldnt tell the barn owner anything, Id just tell the pony owner sorry but I don't know my schedule so not really comfortable being responsible.
You are the customer also. If you went out to dinner and the next table's food wasnt right would you go into the kitchen and cook it for them? Its a barn owner horse owner issue.