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I'm really sorry I don't think I have made myself clear. (I often babble

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The yard owner does not teach so is therefore not losing any clients.
The instructor teaches liveries at the yard that are paying for use of facilities (inc arena)
If a livery is having a lesson they do not have sole use of the arena. Instructor is often teaching one person whilst others are using the school.
I hope that's better and makes more sense.
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YO is right to charge..however as instructress is paying(which will show in cost of said lesson),the school should be the insructors and clients for the length of time of the lesson,she has paid to book her time in the school,so therefore YO wrong to allow others in school....they have to book our school out for lessons,if they dont then yes others will use it