I don’t think any summer camps would trade work for ride time. They need real, paid, insured, employees and they have their horses fully occupied with the clients.
So this contretemps with the trainer is very recent, wasn’t the issue when you posted last week?
Honestly, at 14, I don’t think you can just “approach” barns and ask for a work/ride exchange. Or really at any age. You are going to have to go and take some lessons, so that you can evaluate the barn and the barn can evaluate you. After both of you decide you like each other, you can start asking about work/ride/lesson exchange.
But be warned that the exchange is not likely to be in your favor. If a lesson or practice ride on a horse is worth $50 an hour, and barn work is worth $10 an hour, you will need to do five hours of real nonstop hard labor barn work (probably mucking stalls and feeding hay) in order to earn one hour’s ride. You will need to be totally professional about this, and treat it like a real job (be on time, probably early in the morning, no cutting corners, no daydreaming to your earbud, no texting friends or chit-chatting to other barn kids). Five hours of barn labor will probably leave you too tired to ride that day.
Learning how to research things on line is a useful skill. Go online and search for all the barns that are in a reasonable proximity to your house. How are you going to get transport? Will your mother drive you? Will your mother drive you to a job that starts at 7:30 am? Do you use a bike or public transit? Are there barns you can get to without your mother driving you? If you are going to be at this barn multiple days a week, you can rule out the ones that are two hours drive away. You don’t want to leave the house at 5:30 am to feed horses at 7:30 am.
When you find barns in reasonable proximity, have a good look at their websites. See what they offer. See if they take kids to shows. Showing isn’t the be-all and end all of riding, but it is a marker that this barn is able to take beginner kids and instill some level of competence in them. You want a barn that is catering to beginner/intermediate teens on a budget (to kids like you), not a high end Grand Prix jumper barn or a place full of middle aged dressage riders.
When you get a short list of barns, then go and take a few lessons at each.
Your former trainer will be a good guide to the local scene as well.
As far as reputable, there will be a trade-off here. A really reputable barn that is making a decent income will hire its staff, pay them, and charge its clients for lessons and training in a way that lets the barn pay its employees.
The barns that need to cobble together multiple teens doing work/riding barter to keep the place going may have many positive aspects, but in general they are going to be more economically marginal, and probably have a less coherent program. In other words, what you are looking for is going to be harder to find in a really “reputable” barn, and easier to find in a place that is a bit sketchy.
It will be up to you to decide how much sketchy you can take.
You are unlikely to find work/ride barter in a top barn. Those places might have “working student” interneships but that’s a very different thing in top barns, at least.
