The first time Roxas is able to dual-wield, it's because he has defeated Xion on Day 357. As such, her power flowed into Roxas, and this meant that he had all of half of Sora's power. Because Sora is able to dual-wield due to Special Circumstances, so is Roxas. The theory of dual-wielding that I'm operating under is that one type of dual-wielding may occur when the Heart of a Keybearer aligns in a special way with another heart. In Kingdom Hearts II, Sora manages this by aligning his Heart with his friends, Donald and Goofy, and thus activating a set of powers called a Drive Form. However, there are some Drive Forms that Sora may activate <i>without</i> doing such a thing, such as Anti-Form and Limit Form, but Anti-Form cannot be triggered on purpose and as such is likely an accident that happens due to Sora losing his heart in the first Kingdom Hearts, and since Limit Form represents Sora's memories, it's possible that he is synchronizing with his <i>own</i> heart.

It's debatable whether Roxas' two Keyblades belong to Sora, Ventus, Roxas himself, or Xion (therefore making one of them a "fake" Keyblade). However, considering the scene on Day 358 when he threw one of his Keyblades to Riku and, upon catching it, Riku was struck by memories of Xion and he could hear her voice (theoretically, it is Heart speaking to him through it), I'm going to play it as one of those Keyblades belonging to Xion. That being said, it still makes it difficult to say for sure whose Heart Roxas was synchronizing with.