For one Maul challenged Sidious's title by calling himself the true Sith lord and taking an apprentice. That's a rival. That's something you attack and kill before you are chased out of your pride lands and all your plans for galactic domination go up in smoke. When it comes to something that serious the phrase, "You want something done you gotta do it yourself." comes to mind. Another problem with involving Dooku is he is rather well known as the leader if the CIS. He shows up on Mandalore someone might assume its an invasion. That might throw a monkey wrench in some plans. Sidious also puts some life into the "When life gives you lemons you make lemonade" saying. When life throws a former apprentice at your who should be dead at you, and he proves to be a fairly good tactician taking over some gangs and a whole planet you beat him into submission and use him. Sids was never in any danger himself, that was so one sided a fight it could be in the Robot Chicken sketch.