I've never been lucky enough to have the option of boarding a horse at home. I've always had to board at places. I'm pretty happy with where I'm at now. It is a little run down, but not super busy. Everyone who actually boards horses out there I get along with (there aren't very many). There is one leaser that I can't tolerate, but if I avoid him, everything is ok. Have you ever boarded at a stable before? Depending on the barn, there are pros and cons. Odds are there will be "that one person" who casues horse drama for everyone else. (In my case, it is the leaser who comes out 3x a week) You have to be prepared to deal with people you may not get along with, where at home you have the comforts of being around people you actually like. You also have to consider any conflict you might have with your cousin. I've heard many stories of best friends that rent an apartment or room together end up hating each other. The same can go for two people sharing a horse. Events might come up. Technically, he will always be your horse, you own him and "have full rights" to him as far as major decisions go. Like you can always choose to bring him back home. If both you and cousin want to be using him in events and play days, I'd absolutely set up a schedule of when she can ride, when you can ride. Like you have m/w/f and she she t/th/s. (Not that Ir eally think your horse should be ridden 6 times a week, but you get what I mean). As for play days, switch off. You take the first one, she has the next one, etc.
So those are some cons. You also have to consider conflict with the barn owners and managers. Have you see the barn yet? Talked to the people? Walked around and inspected hay and fences and stalls for quality control? If you haven't I'd do that first.
Then, assuming you are pleased with everything at the barn, and you and your cousin have worked out a schedule of who rides when, and you still want access to trainers and advice and an arena, then I think it is really up to you. Not that I'm saying you should say, "Screw you, husband!" but more like sit down and talk to him and ask him important questions like WHY he is opposed to it. If he takes no interest in the horse, why does he think you can't learn anything at this barn? Why does he think (and be demanding in getting specifics, don't just accept "cuz my coworker said so" ask WHY the coworker thinks these things. Mainly ask for examples!!) your horse will get sick? Make him realize that none of that is true, horses get sick everywhere! I'm sure your horse has been sick or injured at one point in your owning him. And "riding in circles" is necessary for teaching your horse to do things. You can't run a barrel pattern anywhere at all whenever you feel like. Things like Barrels need to be done in an arena. Try explaining you have desires to fulfill with your horse that you can't do at home. As for your confidence, while I don't know why it isn't as strong as it used to be, I don't think it is a good idea to push a non-confident rider to do something they don't feel comfortable with, without some kind of supervision. While I do think that you need to "push" a rider past her comfort zone in order to grow as a horse person, if you are riding alone near ditches and ravines and you don't feel comfortable, then you don't feel safe. If you don't feel safe and try it anyway, it can result in horse and/or rider injury. Now, if you are riding on the trail near ditches and ravines WITH someone, then that person can not only tell you if you are doing something wrong and/or dangerous, but can help you by showing you that riding there is safe and ok. When training a horse to go out on the trail, typically a "buddy horse" goes with the inexperienced one to help the horse gain confidence and know that it is ok. The same exact method applies for people too!
Just my two cents. I hope you can work something out that is going to be the best for you and your horse! Good luck.
~He knows when you're happy
~He knows when you're comfortable
~And he always knows when you have carrots.