Hello. Welcome to Just Answer.
For a 60 amp feed, #6 wire is fine.
The distance, at only 16 feet, is a non issue.
You won't have a voltage drop problem at all.
The #6 wire needs to be protected by a properly sized breaker (relative to amperage rating) at either end.
Since you plan to feed that wire with a double pole 60, you are fine connecting the other end of it to a double pole 100.
OK. Everything you've proposed still sounds fine though. I see no issues with it at all.
Do you have any other questions?
Sounds good. Thank you for the opportunity to help. Have a great night.