I had one horse, who had suspensories so messed up I couldnt ride anymore. I had him for about a year just as a pet, after I spend four years riding and showing him. I told him I'd keep him forever. No one really wants a lame horse, who require $250 custom made shoes every month, well no one would take him that I could trust to keep him. I kept him untill 2004, when we decided to put him down because he had extensive neurological issues, and was not gaining weight on anything.
My second horse, has navicular syndrome. She's been on and off again lame for the last two years. Since July shes not been ridden. She isnt a horse I would sell. Shes just to dangerous for nonaggressive riders. She requires alot of transitions and half haults to stay somewhat calm. Her lack of training and her lameness make her almost unrehomable. Shes my baby, she just kind of hangs out in the pasture, her main job is to teach the other horses manners. If I had to I would sell my yearling before I got rid of my mare.
I do understand that some people just really want to ride and show and have a horse they can show off. And they just can afford two. But I just dont have the heart to send a horse to someone else who has given me so much love and trust me completly.
If I were in your situation I would keep nelson, if it was feasable, and I would start searching for a horse who could take me places, or a lesson horse I could compete with, and ride nelson for fun, if it turns out he cant hold up. Of course I am assuming you lessons would be the same price on another horse, and you could find a horse to ride for free.
Sometimes having a horse you cant ride is pretty heart breaking too. I used to watch the local dressage shows. But I just cant go anymore. One time I went, we were in the parking lot and I just couldnt get out of the car. I wanted to ride soo bad. It was so depressing to watch a show and know you could never do that with your best friend anymore.
I have my two, I wish I could afford more. The only reasons I can really afford both of them is because I dont pay for a place with a ring, or hot water, or full service/care. I
For stall kicking, I would probably keep him outside, with access to a large run in (of course this may not even be possible in your area) see if he still kicks. I hate shifting around to different barns alot, and I like to stick with one place if they have good care, but maybe you could continue with your instructor, but more nelson to a less expensive barn, assuming it still has good care, and use that extra $$ to pay for more lessons, or contribute to nelson's "extra things he needs fund."
Althought I know were I live its hard to find good care, a good barn, and a good price, unless you work off board or know someone.