Contrary to what you'll likely read about, the Economic play style requires the least amount of strategy of the three (IMO Military is often the most taxing while Religious is a close second).
Nevertheless, out of all my years of enjoying Spore I have noticed a few things about Civilization strategies in particular. Mainly, the only "best" thing you can do when a nation contacts you saying they don't like the fact that you're trading with their enemy, it really just boils down to who you feel you can handle disappointing the most.
For instance, you can try to consult your mini map before giving the nation-in-contact your answer. Count the total number of cities they are in control of - the less they have, the greater the chance that they won't be much of a threat at all and thus, making "no" the safer answer. If, on the other hand, if said nation has several cities (or more cities than the nation you're trading with at least), then there's fair chance you can get away with cutting your current trade deal and be able to prosper with this new potential trading partner.
One final rule of thumb is that if you're thinking about cutting your trading ties to please the nation that wants you to stop, more times than not it's often a good idea to just agree to their trade cancellation request without asking for money; this way, they'll respect you so much more and will be more willing to trade with you from that point on (whereas if you agree but ask for a 4,000 sporebuck reimbursement, you'll basically just earn a newly offended enemy and only have a weak amount of pocket change to show for it).