Hello! I think my thinking is right, but I would love some clarification for this question. I think major product has two alkenes, but wasn't sure how to go about the other OH, if it is internal nucelophilic attack, for example

I originally thought one product would be result of formation good LG, then E1 elimination to alkene. When tertiary carbocation forms, could other OH group attack electrophile?

 This is different approach, but the ideas are the same as what we did earlier.

Protonation of the alcohol converts it into a good leaving group.

H₂O leaves, forming a carbocation. This carbocation then undergoes rearrangement to give a more stable carbocation adjacent to the oxygen of the remaining –OH (stabilized by lone pair of oxygen). During this process, ring expansion can occur.

Ring-expansion preference:

If the rearrangement would expand a 6-membered ring to a 7-membered ring, that pathway is generally less favored (more strain / less favorable geometry).

If the rearrangement would expand a 5-membered ring to a 6-membered ring, that pathway is favored because a 6-membered ring is typically more stable than a 5-membered ring.