I Is it possible to distort a black hole's event horizon

I know this is (probably) not going to work.. But I can't figure out why not :-)

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?
 
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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?
No.

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
No, that's not correct. The reason the early universe didn't collapse into a black hole was that it was expanding rapidly.
 
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It is instead possible if we have 2 colliding black holes to get energy out of the collision in the form of GW.
It's possible that what is left of your "probe" (or at least parts of it) could have been converted into gravitational waves during the collision.

https://en.wikipedia.org/wiki/List_of_gravitational_wave_observations
https://en.wikipedia.org/wiki/Gravitational_wave

Like on 14 September 2015 from 1.3 billion light years away distant merger of two black holes,
36 solar masses and 29 solar masses, resulting in a 62 solar masses black hole with the rest of 3 solar masses = 5.4×1047 Jules "radiated" as gravitational waves.

Accurate simulations of black holes merger can help you understand what and how things evolve during such an event.

I recommend you this lecture like article http://www.ihes.fr/~damour/Conferences/Damour_2body_EHLERS2010.pdf regarding "The Two-Body Problem in General Relativity" by Thibault Damour from Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette, France).
 
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It is instead possible if we have 2 colliding black holes to get energy out of the collision in the form of GW.
The GW radiation does not come from "distorting the event horizon", at least not if you interpret that as allowing anything that was inside the horizon to escape. Nothing that once gets inside the horizon can escape (at least not if we are talking about classical GR, which I assume we are in this discussion). The GW radiation comes from the merging of the horizons of the two holes into one; the initial merged horizon is not symmetrical, and the asymmetries are radiated away as GWs. The energy contained in the GWs was stored in spacetime curvature outside the horizon(s); it does not come from inside.
 
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@PeterDonis : I concur.

Also using multiple collisions with what remains from previous collisions (maybe 3BP- 3body problems or why not - 5 or more - colliding BH) - aka complicated collisions between multiple spinning BH (anyways, all BHs actually do have some spin, but we approximate this in some certain conditions in order to get simpler equations) - could be "engineered" to release great amount of energy - like half of total mass of all BH inflicted (?) maybe even more (or less). Engineered aka not quite "natural" occurring or rarely occurring in nature (merging of multiple galaxies ?)...
 
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half of total mass of all BH inflicted
You can get close to this if you take two non-rotating holes and merge them in such a way that the final hole has close to the maximum possible spin for its mass.
 

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