This sounds awfully complicated. Let me give an example of the Mirrer Yeshiva in Yerushalayim and see how the ‘oilem’ takes it.
When Rav Beinush Finkel zatza”l was nifter, His son in law, Rav Noson Zvi Finkel zatza”l was appointed Rosh yeshiva. At the time, Rav Refoel Shmuelevitz zatza”l made a quiet protest on behalf of the Shmuelevitz branch of the Finkel family. Perhaps as the eldest son of Reb Chaim zatza”l he should be appointed R”Y. The case went before Rav Schach zatza”l. He asked R’ Refoel, are you willing to take on the financial burden of the yeshiva?, and the answer was no. So all agreed that R’ Noson Zvi be appointed.
In true Mir style, R’ Noson Zvi insisted that R’ Refoel share the weekly shiur klali, and 5 years ago when R’ Noson Zvi was nifter suddenly, all supported his son R’ Leizer Yudel to take over the yeshiva. (Perhaps cynically, the overdraft was so big, no one else wanted it). To this day, R’ Leizer Yudel and R’ Refoel’s son share the weekly Shiur klali. This is even though there are older (and perhaps greater – but who can judge that) talmidei chachomim in the yeshiva.
My point is, that being a relative of the previous rosh yeshiva does help, but the leadership is not all the kovod, but goes with the responsibility of raising the money.
What is very sad, is when bochurim or other people take sides in a dispute. That is what was destroying Ponovezh a few years ago, and sadly sadly continues in other places, not only yeshivas, but communities and rebistivas (Chasidic courts) where it can and has torn apart families.