I'm struggling to get past the daily race hard mode. What horses are best for getting first place in the money one in particular?

Are my horses actually getting better through repeating careers? I got a 3 speed on another horse and have been using her as parent fodder but I don't actually know if my horses are improving. am I just grinding to get two 3 speed horses and using them for everyone? When can I get to the point where I don't have to treat the middle three stats as total dump stats?

Okay, so for training I want to spam train one or two horses until they give out really good bonuses to the other horses right?
This is my lineup. Who are the ones who I should specifically be spamming training with to become teachers? Also, I'm pretty stuck with Silence and with Vodka, I want to use the two of them but I'm not entirely sure who they make redundant in my crew. Is Silence a straight upgrade to the dumb one and is Vodka a bad pink smiley?