Re: spacecraft design
"The first stage bumped into the second stage, which blew up said second stage..."
Not quite - the R7 series of launchers have a central 'core' section, that forms the 'first' stage, to which are attached four discrete boosters. Thrust from each of the four boosters is transferred to the 1st stage core by a 'ball' at the tip of each booster, which sits inside a 'cup' that is built in to the side of the upper section of the core. The base of each booster has a linkage to the core, to retain the booster and keep it in place alongside the core, but which transfers none of the thrust. This arrangement, that of transferring the thrust from the boosters to the core at the core's upper section and not at the base, means that the lower section of the core need only be strong enough to cope with the thrust from its own engines and not the entire thrust of the launcher.
When the boosters have done their work and are to be jettisoned the motors are first shut down and then the lower links are relaxed, allowing the booster to swing out at its base and drop back a little and this allows the thrust transfer 'ball' to drop out of the 'cup' on the side of the upper section of the core. After the ball has dropped out of the cup, small thrusters built in to the tips of each of the boosters are then fired to swing the tips of the boosters out and away from the core, the boosters rotating around their base linkages as the tips swing out. Once the boosters have rotated far enough they disengage from their base linkages and fall away.
The problem seems to have occurred when the booster tip thrusters were fired, with one of them failing to operate correctly and resulting in the tip of that booster re-contacting the side of the core, which at that point still had fuel and which was still running.
The second stage sat on top of the core module of the first stage, with the Soyuz sitting on top of that.