From what I gathered, the knights think that she's simply trying to seduce the duke for his money since she's from a no-name baron family.
They gave her the crazy horse in an attempt to scare her off, but the horse ended up becoming docile towards her when she saved it from one of those plant monsters.
The duke finds her but they get cornered by a bunch of pigdog monsters, so they fell off a cliff to the forest below. The duke wounded his head, some time while Grace was trying to find food, these hunting monsters captured them.
The hunting monsters were doing this ritual thing to summon a huge fish monster and threw the injured duke into the lake. Grace saves him and realizes she has a power that makes her stronger than what she already was in her previous life.
After she got the duke out of the lake, she had to do CPR to him. The knight with orange hair and the mustache arrived at that moment and saw it. Thus, he ended up getting more desperate to separate the two. (I don't know if he knows what CPR is but I guess he just thought she was randomly kissing the duke.)