Yeah…I'm sure we could "force" him to retire by some of the aforementioned methods but I would seriously be surprised if that were the case.
Look at the lengths the franchise went to in the past year or two to repair the relationship with Rodgers? Both parties seem to genuinely want to work together (and finish working together, whenever that is!) on good terms. I seriously doubt they would about-face and go all scorched earth to force him out a year later.
That's not good management strategy in general; I know GB has never been the most alluring FA destination but consider the impact such a treatment would have on potential outside FAs, players on expiring contracts, etc...It would be awfully easy for a player to look at the situation and think, "If that's how they treated one of their best players of all-time at the end, how will they treat a guy like me?"
And of course there's some more nuance to that, it doesn't adequately explain the totality of the situation but it would not surprise me if players would potentially view it that way.
That said of course I think there are still some measures you can take to give a bit of a nudge without being disrespectful or burning bridges. There have been some concessions made for Rodgers over the year that were perhaps not the most sound "business decisions" and likely wouldn't have been made if he wasn't here. Rodgers has said he does not particularly want to be a part of a rebuild and if the business decision is made to let guys like Lazard, Tonyan, Lewis, Cobb, etc walk I think the message would be fairly clear.
So all that to say it's a little bit of both.
No, the Packers can't technically "force" Rodgers to retire.
Yes, the Packers could in theory make life so uncomfortable for Rodgers that he would feel "forced" into retirement or a trade request.
No, I don't believe GB would take that approach.
But yes - the team could perhaps start to nudge that direction without relegating AR to being a clipboard holder or "#3 Scout Team QB" or whatever.