I really don't think to Wolverine he sees any contradiction in his actions.
He runs a school and an assassination squad. Yeah, but his reason for killing people is to ensure the kids don't have to. His thought is 'I'm already the killer, as are the guys with me, so we can protect the children and makes sure they don't have to become us'.
On killing Hope, I think he sees the main difference as he doesn't believe children should be made into soldiers, but he's willing to kill her to save the world. He honestly believes it will consume her and destroy everything, so to him killing her is the only option and that he may even be saving her in a way by doing it. He may also be doing it because he realises the others may finally realise it come down to that and he will do it first to ensure nobody else has to even make the call, though this is conjecture on my part, since this isn't entirely confirmed in anything he says (however when Scott ran X-Force, Logan made a point of basically making the actual orders to kill so Scott didn't have to live with it).
Certainly depending on how you look at it some of his ideas a contradictory, but that's part of being human. Every single human will have beliefs that are in direct contradiction to other beliefs, however we all develop reasoning for ourself as to why they aren't. It's just how we are, and Logan is guilty of this like anyone else.