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> the nuclear processes would have to oppose that direction to oppose that motion. How does that work?

Those "nuclear processes" are basically a thermonuclear explosion (think H bomb). How does an explosion know in which direction to explode? Well, it doesn't, it just explodes, and stuff flies the only direction possible, outwards (i.e. away from the center).

You can think of the process inside a sun as being a humongous thermonuclear explosion: A sun is a huge H bomb, continuously exploding as long as it has explosives fuel to burn. Now the star's huge gravity tries to counteract the explosion's "outwards flying" motion, till they reach an equilibrium which determines the apparent diameter of a sun (and explains why this diameter isn't always constant).

You can think of a "supernova" as a perturbation in that equilibrium: In the classical single-star case, fuel starts running out, so the "explosion" weakens, and gravity wins out, compressing the star even more (it gets smaller). This compression allows other, previously inert elements to start fusing (exploding), and that new explosion is so violent it beats gravity and manages to spill the stars innards all over the neighborhood. That's a supernova.

_{Obviously astrophysicists will howl, but this is indeed the simplified, layman version on why stars go "boom" when older...}