If everyone's all in agreement then I don't see any reason not to. I mean, you seem like a pretty down to earth person that wouldn't ask your boyfriend to do anything stupid. So yeah, if the owners are alright with it, and your boyfriend is okay with it, I see no reason as to why you couldn't supervise him while he rides.
Plus it would be fantastic for his own riding skills.
Judging by how you're getting paid to ride 9 different horses, you're probably experienced and have been riding for a while. You have to remember that while you've been on many different personalities and temperaments, he hasn't. As more experienced riders we see things as easy every day tasks, but for him this could be more challenging.
Personally, I don't put riders that get nervous around horses much more than school horses until they get more confident and skilled-- one bad experience can scare them away and they'll never ride again. Keep in mind that he's a novice and you could put him in a potentially dangerous situation. If he gets hurt, it's possible it could really take a toll on your relationship.
I'd definitely talk with the owners and let them know you're injured and can't ride, you can probably work something out such as him lunging and grooming the horses with your supervision for a lower price, and riding the safer ones. The owners may prefer just to hire someone else until you can ride again or take care of it themselves. I'm assuming you're getting paid for sick leave, but there's still a big gap.
If your boyfriend isn't already working extra, see if he can work longer at his job until you're better, or see if someone can loan you the extra money until you're better. Hope you get well soon.
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