I'm planning a trip with my friend without another friend.
Why aren't you taking your other friend?
I hate my other friend, he always starts a scene and is unnecessarily rude towards others.
If everyone going on the trip feels the same way about them, then you don't need to feel obligated to include them. It's obviously polite and expected to invite friends to places, but it doesn't sound like he's a very good friend if he is always rude to people.
He's a jerk and a known troll in our group of friends.
Then it may be best to not include him in the trip. It may make things awkward if he finds out he wasn't invited, but that's better than him potentially ruining the whole trip. If your group of friends doesn't like him though, you should all consider just removing him from your circle of friends.