So here is the theoretical situation...

Lets say we have 2 black holes that, somehow, we can perfectly control (velocity, position, rotation etc. etc.).

Now, one of my probes accidentally falls into one of the black holes and I really want it back..

Could you use the second black hole's mass (and corresponding space-time warping) to distort the first black hole's event horizon enough to get to the probe?

From what I've gathered, the reason the very-very early universe didn't collapse into a black hole is because the gravitational warping of space time was uniform enough not to collapse into a black hole - i.e., the gravitational pull was equal in all directions.

My idea would be that the above situation would be somewhat similar - the gravitational bending of space time caused by the second black hole could be used to interfere with the gravitational bending of the first black hole, causing the event horizon of the first black hole to be pushed inward. And, if so, could we use that to "uncover" the black hole and retrieve something that fell into it (very recently)? Or is there some kind of general/special relativity mechanic that I'm not taking into account here?