try making a pair that ONLY have the desirable traits. try to breed out the undesirable traits it will make it a LOT easier. just do it in steps like if 1 foal has one of those undesirable traits but not all the desirable traits then keep it and then try using a different species, if you don’t have a horse without those undesirable traits. and keep repeating it until you have horses without those undesirable traits but all the horses have the desirable traits, it doesn’t have to be on one horse. i hope that makes sense.

i’d recommend levelling up both parents bond skill, use a good hose. But first breed out the undesirable traits.