Just so we know...what exact computer models are we dealing with (wife's computer & your computer). I know the thread title says "Mac Pro"...but there are a lot of different Mac Pro models. And hopefully you're referring to a "Mac Pro" desktop computer...and not a MacBook Pro (which some folks mistakenly refer to as a "Mac Pro").
In any case...I'm pretty sure the computer model shouldn't make a difference. And as you saw...the "Sharing" system preference is on your wife's computer running Sierra. The only explanation's I can think of why it's not on your computer are:
- a file or files got accidentially deleted
- a file or files have gotten damaged
- a file or files were moved out of the folder where they belong
A couple thing's you can try are:
- Do an NVRAM reset (internet search for the procedure).
- Run the free maintenance app called "Onyx". Maybe if a file got damaged or a permissions file got damaged...it can repair it.
HTH,
- Nick