Why did Tobi let Itachi remain in Akatsuki? Tobi was well aware of Itachi's true motive for joining Akatsuki. He knew that Itachi massacred his entire clan only for the village's sake. 


  Then why did he let Itachi join the Akatsuki?


He was also aware that Itachi was trying to protect the leaf village from Akatsuki. So my next question is 


  Why didn't he get rid of Itachi at least after they start to capture the tailed beasts?
He let him stay because a lot members of the organization had their own motives and knew they would betray the overall effort at some point or another.  They are all missing nins which means loyalty to an organization was clearly not on the top of their list.  Many were even there just to spy or further their own goals.  It didn't matter to him as long as he can use them to accomplish immediate goals.  And everyone of them thought they would eventually outsmart, control or win over the others as they are all excellent ninjas.  


Pain/Konan revealed they never intended to go along with Tobi's original plan. Tobi was aware of this at least to some extent.  There was clearly mistrust between the two. 
Orochimaru was a big time defector and they always knew he was there to spy on them and had his own agenda.  
Kisame only went along with Tobi once he revealed he was the real Mizukage. Otherwise it seems like he didn't really have any loyalty other than it was what he was doing at the time. 
His alliance with Kabuto, he knew he couldn't trust him but partnered with him anyways because of all the reasons listed above.  


He also didn't think Itachi knew as much as he did or was good as he was (a testiment to how good a ninja he was).  Also he liked the idea of having extra Sharingans hanging around in case he needed them.