What is mixed in with the gold to give it its rose color?
Copper. It's not so much as what's added as it is in what percentages. To the best of my knowledge all gold used in watches contains gold, silver & copper. White gold adds Palladium or Rhodium as well. Each manufacture is a little unique on percentages I'd imagine, but an example would be the following percentages:
Yellow gold = 75% gold, 16% silver & 9% copper
Rose gold = 75% gold, 9% silver & 16% copper
And a white gold example would be 75% gold, 3% silver12.5% palladium & 9.5% copper
But like I said, those are examples (from Breitling). There's probably dozens of formulas (and I have no idea what Rolex's is). The percentage differences is also what makes some rose golds look very subtle and some look more harsh.