Read all of this, interesting situation that turns up, sooner or later, for any Pro. How they handle it can be a personal, career defining moment. Choices can be difficult and are rarely clear cut.
My thoughts are that this situation is just not something OP can work with within the parameters set by the client here, meaning the parents. You can’t fix everything and everybody as a Pro. Short and simple. Forget the horse, most can be fixed with consistent, goal oriented programs. It’s the humans who refuse to commit to any kind of consistent program be it twice a month hauling in or traveling to them with homework to be mastered before the next visit or full time boarding taking two or three lessons a week. Even full training, horse get better, owner gets on, does not follow direction or know how, training goes poof. That you can’t fix and this type owner/parent WILL blame you.
I get the can’t afford it angle, BTDT the first 25 years I owned horses starting at age 18, BUT I was committed to getting quality instruction less frequently (twice a month) and diligently doing the homework. And watched and listened and hung around the barn and local show schooling rings learning, This kid doesn’t, maybe because parents won’t take her or can’t afford even twice a month haul ins. But OP CANT fix that part.
As I read what OP has posted, perhaps there are some personal feelings here, Pros are humans too, there’s no path to success here without a change in attitude on the client side. OP seems to run a barn that tries to work with individual limitations but this situation goes beyond what she can work with given the lack of commitment. All else aside, if they aren’t there and won’t listen when they are? What’s the point? There’s no tools or cooperation to work with. You not a miracle worker, they don’t listen so stop beating your head against the wall, let them go. Perhaps they will work it out with another or perhaps not but let them make the choice to follow your program for them or go elsewhere.
But HOW to let them go without creating a kerfuffle or treating them any differently then your other clients as the last thing you want to do is single any client out. My two very best trainers over 50 years both did the same thing, annual sit down goal meetings with each client, haul ins, non owning lesson takers or full time in barn clients/parents. Yes, it will take a few minutes more of your time per client but creates a much better understanding and defines expectations on both sides. You get a better idea where they want to go and they can share those thoughts with you and feel more valued as a client. You also can go over what you would like to see from them commitment wise besides money.
Might be a good opportunity to review your contracts and barn rules as well as haul in procedures and expectations. You sort of allowed this to get where it is by not standing firm earlier, it’s hard but it is the professional way to conduct a business. Simply require haul ins to agree to a minimum number of sessions a month, like 2, and agree to do the homework. Attach that to your liability release and have them initial or sign it. Reserve the right to conduct the lesson as you deem appropriate, including ground only and stop it if the horse appears unsound or the tack not in good repair or appropriate. The client here has a choice to meet with you and follow your program or not. I would not tell them you don’t have time, tell them the truth, they need to follow your program and your advice or it just won’t work.
Set some guidelines in writing, communicate them with all clients and get everybody on the same page. This will not be the only time you will get clients like these. Don’t be afraid to admit you can’t make exceptions for one client when all the others stay within your guidelines. Or admit to yourself you can’t help those that won’t help themselves.
The way others perceive your talents is through your clients and the condition and performance of their horses. Think about that. Never forget it. And tell the truth, sometimes people actually learn from hearing the truth. Here it’s they follow your guidelines or you do not work with them. Period. You don’t have to fire them. It’s not personal or unique to them and their choice to stay or go. Same as any other client.