When did Kakashi and Obito awaken their Mangekyou Sharingan?
Kakashi and Obito awoke their Mangekyou at the same time: when Kakashi killed Rin.  



Obito (left) and Kakashi (right) awakening their Mangekyou. From chapter 605, pages 4 and 5.  

Now, as for why Kakashi never used it before his fight with Deidara, I think there's no definitive answer. However, I can think of two different educated guesses: one is in-universe, while the other is out-of-universe.  

In-universe explanation: As you said, Kakashi was either unaware of or unable to control his Mangekyou Sharingan. I tend to think the former is the case, since he passed out as soon as he awoke his Mangekyou, and probably had no memory of awakening it (Kakashi's page on Naruto wiki seems to agree with this explanation). If this is the case, after his fight with Itachi he most likely tested to see if he had the Mangekyou, finding out he did, and thus trained in order to perfect its use.  

Out-of-universe explanation: Kishimoto hadn't thought the whole story through. Since Tobi had not made an appearance in the first Naruto series, Kishi had not yet thought about who he would be. If this is the case, then Kakashi's back story had not yet been planned, as well as Obito's. This would make it plausible that Kakashi was not initially planned to have a Mangekyou, since his is transplanted. After the Kakashi Gaiden, however, the important characters are all introduced, which means he had most likely planned for Obito to be Tobi, and about the link between his and Kakashi's Sharingan.