We have two super-massive black holes with the same mass rotating around their center of mass. Now, lets put something very dense at the center of mass. It has to be that it's radius is the Schwarzschild radius. Normally, if there weren't those two black holes rotating, this body would become a black hole. And now my question is: does the Schwarzschild radius differ when the are additional masses around a certain body, or will it just will stay the same? I thought about it because of a question: "why didn't the big bang collapse into black hole?" and the answer was because the black hole forms when there is a dense body in not so dense space or something like that. If I'm wrong please tell me where (I'm just high school student who is interested in physics).
The Schwartzchild black hole is a toy model, that probably does not exist in nature, sorry if you know this already. It does not include the angular momentum of a real star, so all real black holes will be rotating (probably).
The second thing I would like to point out is the Birkoff Theorem, which says the gravitional effect of the mass inside the event horizon will not change if the mass inside expands symmetrically. This is probably unlikely unless the system is set up just right, but I think I should mention it.
I don't know how fast your system is moving, or what relative positions they have to each other (or, most importantly, I have no idea what happens inside a black hole event horizon), but I mention these things because 1. I think you should read up on them, as you don't mention them in your post, and 2. without knowing more about your setup, I don't think your question has an answer at present.
Am I saying, read up a bit more and post a shorter, more focused question, than includes these point? Yes, no offence, I am :) best of luck with it.