Sometimes things in life don't go perfectly. If one of those things is being traded to another team (who has a better chance of winning now) while they still pay you multi millions a year, yeah I just don't see how that is really just that stressful.
If you don't want to handle the "stress" that comes with being traded or speculated that you might be traded, then negotiate into your contract a no trade clause, I'm sure at the time the Twins would have been more than happy to grant Span a no trade clause if he would have accepted a couple million dollars less per season. I mean I imagine it would suck to be traded suddenly and would be an inconvenience to find a new place to live etc, but the nice thing is you would have plenty of money/help in order to get you situated quickly.
I feel a lot worse for the throw in minor league guy who gets traded and is only making 50k a year.