[Itasan]

Wow! Very interesting, but difficult. I wonder if the difference is
whether the trip is required or on your own.
1. The choice is yours. You can take the trip if it suits you. But you don't need to.
1a. It takes a certain amount of time for the trip, whether you want it or not.
2 and 2a are completely different, right?
3. You HAVE TO go if you want to get your tooth fixed.
4. You are required to go.
4a. It's an order, but Peter has the option of declining.
Is this understanding correct or close or totally wrong?
Thank you.