But why take her elsewhere, then? Why take her anywhere at all? He could have killed them both at the house and left them there.
I agree, nothing really makes sense. The whole thing's illogical. I struggle to believe it was an orchestrated plot involving the mother, even one gone terribly wrong. From all indications she didn't want the kid full-time. She works at a Macs while completing her secondary education online as a mature age student. Doesn't really sound like someone desperate to be an everyday mummy. Best I can come up with, somehow Derek believes either that Hailey is his child, or that TB stole CD from him and that Hailey should be his. He becomes increasingly obsessed with the idea that if he can just remove TB from the picture he can have the perfect little family he desires.
Finally he commits, breaks into TB's house late one night, knife in hand. Unfortunately, things don't go as smoothly as he planned. TB wakes, confronts him, they argue and Derek flies into a mad rage, frenziedly stabbing TB. When he snaps out of it he realises Hailey's seen the whole thing, she's crying her eyes out. He panics, nothing's working out like it was supposed to. He still sees Hailey as a means of winning back CD, however, so his only idea is to just get her out of there and try to fix the situation somewhere quieter.
As he drives, though, he begins to think a little more clearly. He realises there's no way he's going to be able to adequately explain what happened at TB's and why he has possession of the child. He gets desperate, scared. Hailey won't stop crying. He's looking for an out, a quick solution. He doesn't really have a choice. He dumps her body in the grass, goes home, smokes some weed, and then goes to bed.