Well by all means, post pics.
Yes, you're doing the right thing. Horses that just run tend to lose their mind a little bit. We used to get some wrecked horses off the track and use them in the Misouri River Breaks in South Dakota. Usually in the spring time there's a lot of mud and water so bad attitudes and run-offedness lasts about until lunchtime. It's really good for a horse to have off time from their day job too.
Barrel and dogging horses need some rec time too, it just helps them keep their brain from squirming. Just remember that you're riding a race horse and that's their job so any off time should be just that. Race horses going for a recreational ride is like you going for a walk in the woods, it's just nice to get away and not think about work.
Sometimes it takes a little bit for them to realize what's going on, but pretty soon they know the difference between when it's time to run your guts out and when it's time to just be mellow and relax out on a trail ride.
Yes. We got a lot of "ruined" good horses cheap, ride and resell. A couple months behind a cow and their whole world changes. Just remember this isn't a 'cow horse' so you just need to protect her from getting hurt or something because she just doesn't know what's going on yet.
You could do the same thing he did if you even just have an arena or somewhere to ride. Teach her something and work with her every day as much as you can if you have time, it breaks up her day and it gives her an opportunity to do something besides run. 3 months working hard, I bet she's a lot quieter now.

C.