“Why does Lubavitch make such a big deal from winning the machlokes with the Rebbe’s nephew and getting the seforim back in the library, that they’ve turned that day every year into an official Yom Tov? Isn’t it embarrassing to every year revive memories of an internal dispute?”
In few words, because it wasn’t really about the books. It was a question on whether there is a Rebbe today. This was akitrug from shomayim expressed here on earth just like yud tes Kislev.
The reason why the family member was claiming the sefarim was because he held that lubavitch had ended with the frierdiker Rebbe and there was no more Chabad.
So when we overcame that taane it was a big deal and still is today
“Also, why does it seem that Lubavitch has had disputes with an unusually large number of other frum kehilos, both Chasidic and non-Chasidic (Satmar, Brisk?, Chaim Berlin, Ponovitch)?”
Because we have a unique path to everyone else.
“On a lighter note, how can you tell the difference between a Lubavitcher’s hat and a Yeshivisher’s hat?”
I’ll leave that to the men. Probably because we have the brim down, and they put it up