His balance is probably not good and maybe he doesnt have a streng right lead so i would just practise practise practise cabtering around on both sides so make him streng.
To avoid rushing to jumps you Can put one or several poles in front and behind the jump so your horse cant run But have to Think. You Can Also do gymnastik Lines. I would just for a while practise the right lead get your horse to listen do loads of transitions. Then jump a jump relaxed and instead of repeting the exercise over and over just pop over the jump and ride around as if you were flatting. That Way your horse doesnt get exciting or rushes!
Hope that helped