If you upgrade to First, seat assignments are free, but 1A/1K is blocked for Golds.
If your wife is on the same booking then she will benefit from your free seat assignment. If your wife is on another booking (?) then you could ring up and ask for the bookings to be linked, and say "by the way does she have a seat assignment" and the agent may decide to throw you a favour.

As to changing FF partners, it always has a degree of risk. Generally, what I do is play with the manage my bookings through (a) go to RJ.com and physically delete the FF number, (b) reload RJ.com to ensure it is gone, (c) login into BA.com, check that there is an "enter FF number space", enter the number, (d) go to finniar.com to get a pdf emailed to me and then check there is on the FF number that I want, then (e) call BA and have them check there is only one FF number. I know it is quite an exercise but having the wrong account credit is far worse. Calling BA at the first point to ask them often results in (a) two numbers being added, or (b) them saying, oh you upgraded, used points or whatever and you cannot change the FF number.