So, I wonder what changed to have the Uchiha conspirators suddenly turn on Obito and screw with his plans? Just normal AU stuff and not anything Naruto/the Tome did?
Madara wanted to end the rest of the clan for betraying him by not supporting him after the village was founded and Obito was convinced to help with that. In canon that led to the massacre.
Here, a number of things changed when the Tome woke up. Naruto was revealed as a "decoy", which threw Danzo's plans for a loop. He adjusted towards "find the real weapon" as a result. The village as a whole got a lesson in seeing beneath the underneath, as it was, upon finding out that Naruto
couldn't be the fox because he was the
fake...add in that he's likely an actual Uzumaki due to the chakra meter on top of that and they were primed to hate someone they shouldn't have ever had a problem with. Pressure via distrust of the Uchiha dropped at that point on the basis of evaluating what opinions were actually their own and changes in village security patterns further kept Danzo from getting access to Shisui before he and Itachi met up with Jiraiya outside of the village.
Obito, knowing about the coup attempt, then has a new problem that he didn't in canon. He and Zetsu
can't find the fox. At all. And the coup is likely to kill everyone in the village that has any clue where to look. So he figures that he'll slip in and convince the clan to help him find the fox, perhaps claiming that it would allow for proof that he-as-Madara had been framed or something like that. Only he missed that the adults of the clan hated
Madara more than
Konoha, somewhat rightfully blaming the wayward former head of the clan for their troubles.
So instead of joining in on Itachi getting false orders from Danzo to eliminate the clan in their sleep, Obito drops into a room with all but three adult members of the clan that have a justified bone to pick with Madara, who Obito is pretending to be...
Though with that we're still running into fanon/poorly researched canon elements that we're just going to have to call out as AU elements, again. It's at least implied in canon that the once-per-decade thing was more because the eyes weren't held by Shisui/implanted in an actual person anymore. Mostly in that there's no mention of such a large limit when Danzo is abusing his one in the kage summit, and implied to have used it in the past, only later with the one that Itachi stuck in a crow and stuffed down Naruto's throat.
Edit: also, the fact that it was a thing Shisui's eyes were even known to be able to do, when he was a pretty young guy who wouldn't have had time to learn and test the technique, and also have it available to be dangerous at the time of the coup if he had a 10-year cool down on it.
Danzo was supposedly able to spam things by virtue of integration of Hashirama's vitalizing cells supercharging recovery across the board for him, which is essentially another way of saying "bringing it closer to the Rinnegan instead of the Sharingan" from a dojutsu point of view.
As for how they knew things, I personally like the explanation that different Mangekyo reveal different parts of the stone in the Naka Shrine. Specifically, that some of the information you get to see is the basics of what abilities your eyes now have so that you have some kind of clue how to (or not to) use them.
While it's rumored that most of the Uchiha are dead, he put in those that went to that clan head meeting were dead. I've a feeling that many more Uchiha survived this time around. Say, wives and kids that didn't usually go to those things. Shisui, Itachi, and Izumi might have all been missing as well.
Kids were generally not at the meeting (Sasuke was kept unaware of the coup, so we can assume that kids just didn't attend) but there's no reason to keep even civilian adults out of a meeting that involves the clan as a whole.
But we can assume that the three mentioned weren't present.