Well, I think you just answered the question of why the breeder crossed a Bouvier with a Poodle... Very few reputable breeders will breed crossbreds. If they do, it will typically be to either produce serious sport or hunting dogs, or else try and correct a health problem in one of the breeds.
As mentioned, a lot of dogs, once they mature, start to become either very selective about what dogs they like, or just generally dog aggressive. Some breeds are prone to same sex aggression (I'm pretty sure that Bouv are one of them), and no amount of neutering or training can stop it. Even in breeds not generally known for SSA, having multiples of the same gender can still be problematic.
While I'd separate them for feeding and not leave toys laying around, keeping a log of when it happens, what's going on right before it happens, and what happens afterward can be a good idea.
One other thing to touch on is pack dynamics. Two dogs can get a long fine, but adding a third changes things. It could be that one of the established dogs decides they don't like the newcomer. It could be the newcomer deciding that they don't like one of the established dogs. Even if the third dog is added as a puppy, there is no guarantee they won't grow up to hate dog number one or dog number two, or even both of them. And as an FYI, having to live in a crate and rotate situation is no fun. I've done it (twice), and hope to never have to do it again.
