Colonel SP Meek, author of Frog: The Horse that Knew No Master and a whole bunch of dog stories, had one. Belfarm Star or something like that. It was the classic horse gets hurt, and only the one person believes in him/understands him/inspires him to get better, which of course he does, and they go win the Big Race. Formulaic but nice reading.
There was also one, but I can't remember the author or title. I remember the horse. His name was Snow Prince. Story of a struggling farm/lady trainer, and he was her best upcoming prospect and literally the great white hope. Ring any bells with anyone?
Cherokee Bill (although it's about a pacer and NOT a racehorse). There is also another one whose title I can't remember---horse not doing well as a trotter, and then owner/trainer and/or boy discovers when horse "breaks", he breaks into a pace. Voila!
"Oh, sure, you may be able to take down one smurf, but mark my words: You bonk one smurf, you better be ready for a blue wave."---Bucky Katt
You only have part of the Belfarm Star story. Indeed horse breaks it's leg and younger brother threatens vet with a pitchfork and then rigs a sling for the horse and cuts a hole in the floor for injured leg to dangle until it heals. Older brother is in World War 2 and younger brother has a club foot and wants to be an engineer but accepts responsibility for managing the horse for older brother while he is gone. He eventually rigs a shoe extension so he can actually drive and changes the horse from a trotter to a pacer. So he takes her to the Little Brown Jug instead of the Hambletonian. Of course she wins and the older brother is there in the winner's circle. He offers the horse to the younger brother but he wants to go to college.
My father worked for a newspaper publisher who had a standardbred breeding farm. We grew up on harness racing books. More than once we've looked up the White racing stable at the Lexington Trots after reading Born to Trot.
Some other harness racing fiction books for children include:
The Phantom Filly by George Agnew Chamberlain (1945)
Lord Buff And The Silver Star by George Agnew Chamberlain (1955)
The Good Luck Colt by Genevieve Torrey Eames (1953)
Old Sam, Thoroughbred Trotter by Don Alonzo Taylor (1955)
Red Horse Hill by Stephen Meader (1930)
Cedar's Boy by Stephen Meader (1949)
The Horse Comes First by Mary Calhoun (1974)
Small Gains by K.M. Peyton (2004)
To Race A Dream by Deborah Savage (1994)
There was one I read in elementary or middle school for a book report...I felt so lucky that there was a horse book on the teacher's list of options! What was it called...AHA! Thank you vacation1, it was "To Race a Dream."
"Shame the Devil" is a great story about drug dealing and backstretch intrigue at the harness track, though it didn't get very good reviews - I still like it. I certainly prefer it to the Dick Francis string - I call those one-hour books because that's all they take.