[IAmBroom]

I think you're playing fast-and-loose with the notion of "colliding".

First define what you mean by "colliding".

By analogy, I'm defining it as the Event Horizons intersecting, at which point nothing in side "either" black hole has any physical meaning to us ever again. For all we know, the insides could be chocolate ice cream on one half of the now-double-sized Event Horizon, and pure neutronium on the other. It's meaningless to even pretend we know anything about that volume.

[thaumasiotes]

Collision occurs when there is some sort of interaction between massy particles that try and fail to occupy the same space. Whatever stops you from passing through the floor counts as "collision".

An event horizon has no mass or other existence and cannot collide with anything. Within the black hole, there is mass somewhere, but generally not at the event horizon. If you're not comfortable assuming that, we can make it a definition - take this to be an example where none of the internal mass lies within the region of overlap.

What is the obstacle to the black holes separating again?