You actually can go independent and sort of unite the houses, but it's pretty iffy. You not only need a high reputation with all factions, but you also have to bring up the topic with the Iscari and Randal before you declare your alliance. If done right, you can pick "My rebellion!" and Randal and his group will save you, though there will still be a fight because Saorise and Andrei will not give up that easily. So it basically plays out like siding with the Mavvar, only that at the end you are in charge with Randal as your right hand instead of the other way around, and the remaining vampires in the city are more diverse instead of consisting mostly of Mavvar. So, yes, you can bring the three houses together, but not peacefully. There will always be a final clash and Saorise and Andrei will never accept you.
As for your question, you have to be in the same house as your mentor to get the special endings. Those are not necessarily the best endings, mind you. I found Randal's special ending horrifying and Heath's was a tragedy. Only Markus' special ending has an uplifting note. Mind you, you have to get the former two before you can unlock Markus' special ending (which I consider the "true" ending, btw).