Is it possible to enter Thailand for 60 days, leave for a week, and re-enter for another 60 days on a holiday visa?

Should be fine

You may have a hangup with your air carrier. Some want to see a ticket out of Thailand within the number of days allowed by your entry scheme.

With no visa that would be 60 days regardless that you could get an extension.

Some insist others don’t seem to care. Ask yours for their policy or be prepared to buy a ticket out upon check in to be able to board your flight.

Entirely possible if you’re from a country that allows visa exempt entry. Your profile suggests you are.

No one can confirm if it’s going to be without hassle as entry is up to an individual immigration officer. If they’re having a bad hair day then you might get questioned or at an extreme denied. The latter probably won’t be the case but it has happened.

Yes no problem