Changing disciplines is not a good idea because the stats don't get redistributed to the stats for the new discipline. Meaning a horse that has had their discipline changed has lost out on training time compared to other horses. 

As for horses doing worse after training, it might just be that your horses ranked up and are competing against higher tier horses. 

Agree with the above, but you should check your horse’s stats. Sometimes the horse is better suited for another discipline. Or you could switch to a discipline with similar stats but less popular. Western Pleasure, for example, is a good alternative to dressage which is usually more competitive.

Ideally you want to train your horses in the same discipline(s) consistently. For example, all my Mustangs are Trail and Endurance trained. Frankly if you're trying to earn money quickly as a new player I would not recommend the Discipline path as you want horses with good Breed Standards and high Performance Stats, both of which foundation horses (or horses people sell for super cheap, generally) are not good in. If you focus on just throwing all your horses into the career paths you do have access to you will make money far quicker because there's zero entry fees to worry about, just pure profit. That way you can save up and either buy the good horses for disciplines or over time, breed your horses for better BS and PS.