possession with an entity which uses parenthesis

Ugh.

It's a tricky one, but I can certainly rule out the way you have phrased it there.

I would plump for: "Bobby Thompson's (Rutter's) officials have agreed to ..."

In Dave's example it is not clear if (Rutter's) refers to possession of Bobby, or possession of the officials. Unless you must have the apostrophe, why not do it like this:
"Officials of Bobby Thompson (Rutter) have agreed to ..."

Slemmet's solution is the proper and elegant one. It's not clear to me whether you should use "Officials of..." or "The officials of...," but that's a quibble you can quickly resolve.

Yeah, you're spot on about the ambiguity of my rendering. "Officials of Bobby Thompson (Rutter)" it is.

There's no agreed solution for possessives of this type, unfortunately.

They occur quite often when describing an actor's role in a film.
Three possibilities:
A. Don Vito Corleone's [Marlon Brando] offer.
B. Don Vito Corleone [Brando]'s offer.
C. Don Vito Corleone's [Brando's] offer.

Fowler's suggests 'B', deems 'A' legitimate and discourages 'C' as being 'over fussy'

Option B reads better, but it seems rather unusual to have apostrophe-s attached to the closing brace.