I think maybe a cool way to handle it would be you do an extended skill challenge for that player. Each day they get to make one roll. After a few days they either succeed and break in the mount or fail and the mount can't be broken. In the meantime maybe you can still ride it, but the DM might set some restrictions on what you can do, like the mount will always misbehave in combat (doesn't allow you to move it and tries to throw you off each round). That way you have some use of it, you get to ride it for purposes of travel, but it isn't useful in combat until you beat the skill challenge.
I don't really have a problem with characters having personal challenges. Sure, its something the rest of the party isn't participating in but its also not going to eat up a lot of time, especially if its spread out so its just a die roll every so often. As a simple challenge of complexity 1 its a max of what, 7 rolls? Not a big deal.
