I have two units in base, and my opponent has two units in base. My opponent casts Star Crossed targeting one of my units and one of theirs. I cast Rebuttal, and take control of Star Crossed. Can I reselect only the "enemy unit" portion of Star Crossed to target my opponent's other unit? If so, do one or two units return to their hand?

Yes — you can retarget just the enemy-unit portion, and two units total go to hand (one yours, one theirs).

When you take control of Star-Crossed via Rebuttal, "friendly" and "enemy" are re-evaluated from your perspective. Your originally-targeted unit is still a legal "friendly unit" for you, so you may keep that choice and remake only the "enemy unit" choice onto your opponent's other unit. Rule 753 lets you remake any subset of a finalized spell's choices as long as the result is legal — you're not forced to change everything.

You cannot choose only an enemy unit, though: Star-Crossed's "a friendly unit and an enemy unit" is mandatory, so the friendly slot must stay filled (one of your units). On resolution, both chosen units return to their owners' hands — your unit to your hand, and the opponent's other unit to theirs. That's 2 units returned (one per player), not 1.