Once Arjun got to Mathura (some accounts have it as Indraprastha, but I've read of successors to the Pandavas who moved the capital from Hastinapur to Indraprastha), he crowned Vajra as king, and left Subhadra as the caretaker/regent for him (so did the Pandavas leave Uttara to do the same for Parikshit?)
So yes, Vajra ruled the Yadavas after that. His kingdom didn't merge w/ the Pandavas.
Exit question: when the Pandavas did the Rajasuya and Ashwamedha yagnas, what was the status of Dwaraka wrt them? Was it a vassal, an ally or what? In a Rajasuya yagna, the Pandavas would have exacted tribute from all rulers, including allies, but I can't imagine them asking Ugrasena (indirectly Krishna) for tribute. And for the Ashwamedha yagna, I'm guessing there was no way for the horse to get to Dwaraka, since it was an island? Or did Yudhisthir give Krishna the honorary co-host status like he did in the Rajasuya yagna that angered Shishupala? At any rate, what was the status of Dwaraka wrt Indraprastha in both these cases?