However from a strategic point of view, it was not the best call because of these two simple reasons.
Unity is power
Ironically yesterday Scotland voted NO to slipping away from the U.K, which would have otherwise ended a 300 year union. History has taught us that it is far better to be in union with enemies than at dispute with old friends who have the potential to become a thorn. Without a doubt, the president and Amama have egos to nurture and Mbabazi is know for not taking his public image lightly, he demonstrated this when he was paid for substantial libel damages from theDaily Mail, a British tabloid, over an article that alleged his “cronies” took £10m in foreign aid.
Which means his public throw out is likely not to settle well with him anytime soon, leading him to whatever course of action we speculate. There is a famous South African proverb "When you kill a snake, do not swing it in the air to show off because there might be others in the bush looking at you." Strategically speaking throwing Amama out might have sent the desired warning or message however it works counter to NRM because it is no secret that Amama had his supporters. The reason NRM has been able to rule this long is because of their unwavering unity to which the opposition cannot match.
For the sake of the party, a more subtle approach would have been more appropriate because give or take, it is now possible for Amama to make friends with NRM's enemies which isn't good for the ruling party or the country.
A powerful leader surrounds himself with powerful characters
Amama Mbabazi's rumored political ambitions must have caught the president off guard to the extent that the National Bank of Commerce, to which Amama had controling interest was shut down, to cut off the money supply. So at a certain level, there is no denying that Amama was an imminent threat in some way, however the way I see it, having strong and powerful people by your side is more effective than surrounding yourself with people you dominate. Because when that moment comes when your authority is in question, you need people around you that are willing to do whatever it takes to protect the status quo, than weak people who will quickly flip over for whoever comes a long with a new proposition.
The true mark of a powerful leader is one who is able to manage a variation of temperaments on a team and the president's action to throw out Amama, might not have been the best move to that effect. And FYI Amama was not really a direct threat because he lacks one key ingredient to garner for the top seat, "Gusto" which the president clearly does.
Of course everything we know is based on speculation. Its hard to tell exactly what is going on behind closed doors. The major difference between Western and African democracy is, in the west, citizens believe the worst in their leaders which encourages them in turn to work towards pleasing their voters while in Africa, we believe the best in our leaders until they let us down which happens more often than not.
I guess the key take away from today's events is..... Life goes on.