Uranus: The Spin In his prog. , on the outer planets, Brian Cox stated that Uranus spins on its side because it once endured an interplanetary collision.
Such a cataclysm would normally be devastating for both planets. Given that Uranus is a gas-giant, with no solid inner-core, why didn't the second planet simply "float" through the gas clouds?
How does a ball of gas become "turned on its side"?
 A: 
How does a ball of gas become "turned on its side"?

I think you may be misunderstanding the composition of the outer planets a bit.  Uranus and Neptune have icy-rocky cores, so they are not 100% gas.  In fact, these two planets are called ice giants, not gas giants.

Such a cataclysm would normally be devastating for both planets. Given that Uranus is a gas-giant, with no solid inner-core, why didn't the second planet simply "float" through the gas clouds?

Again, no, Uranus is an ice giant, not a gas giant.  Regardless, even if it had no solid core, an impactor would still suffer dramatic deceleration due to aerodynamic drag with the dense gas (dense compared to the surrounding solar wind that is).  Even when a hypersonic impacting object hits a solid, the interaction isn't like two billiard balls reflecting off of each other.  The impactor tends to penetrate to a depth roughly equivalent to its diameter if the object it hits is entirely solid and of roughly similar density.  If the object is a solid crust with a liquid mantel then solid core, the impactor easily punctures the outer solid crust and then interacts with the fluid below.  The crust does little to slow down or stop large asteroids at Earth (actually, there's evidence that the crust liquifies during all of this anyways so not even it remains solid), so it's mostly an interaction between a solid impactor and a liquid body.
Just like solids, liquids and gases carry momentum/kinetic energy.  While the mean density of Uranus is only slightly higher than water, an astroid hitting water interacts like it's hitting a "soft" solid1.
The core(atmosphere) is ~17.5%(~82.5%) of Uranus' total radius, which we will assume to be 25,559 km for now.  The mass of the core(atmosphere) is ~0.55(13.4) Earth masses.  The the density of the core(atmosphere) is ~8.7(1.2) g cm-3 or ~8700(1200) kg m-3.  The average density of Earth's atmosphere is ~1.2 kg m-3, or about 1000 times less dense than the average for Uranus.  If you go deep enough into Uranus' atmosphere, the density is much much higher than water2.
Therefore, the drag on an impactor hitting gas, with properties matching the average atmospheric properties of Uranus' and Earth's, would experience ~1000 times more drag in Uranus' atmosphere.  My point is that when asteroids etc. hit the giant planets, they aren't running into a whispy, tenuous gas that they just pass through.
As an example, consider a ~1 km spherical asteroid impacting Uranus at speed3 of ~26 km/s.  It would experience something like ~2 x 1018 N of force, ignoring ablation, radiation etc.  If the asteroid had the same density as Earth4, then it would have a total mass of ~2 x 1013 kg.  Such a body would experience accelerations of ~105 m s-2 or ~104 g's (only ~10 g's in Earth's atmosphere for comparison).  If we assume the acceleration is constant5, then a ~1 km spherical asteroid moving at ~26 km/s would stop in ~3.4(~3400) km under Uranus'(Earth's) atmospheric conditions.
In short, an impactor would most definitely suffer major deceleration and cause rather dramatic alterations to the angular momentum and kinetic energy of the atmosphere alone, which comprises ~96% of the total mass of Uranus.
Footnotes

*

*ignoring the flash boiling that occurs immediately before collision etc.

*pressure reaches ~100 times Earth's atmosphere at sea level

*I chose a nice round number larger than Uranus' escape speed and near the speed of the interstellar medium.  One can quibble about the actual speed of impactors but above the planetary escape speed is basically fast enough.

*Earth's mean density is ~5495 kg m-3

*This is a bad assumption for many reasons, but mostly because of the following issues: the drag equation depends upon speed squared; it also depends upon density which is not constant with altitude; and at 10,000 g's coupled with extreme heat, a silicate object is not likely to survive in one piece.  A more realistic stopping distance would likely be a factor of ~10-100 larger than the ~3.4 km estimated here for Uranus.

