While Dragon King of Arms may have been justified in his concern that Carrot and Angua would produce an undesirable half-werewolf bloodline, the logical solution for this dilemma for a villain who's willing to kill would surely be to eliminate Angua herself, not to displace Carrot as royal heir or to involve Vimes or Vetinari at all. Whether by arranging an "accident" involving fire or silver, or merely getting her to leave the city, it seems ridiculous for Dragon to have never even considered such an alternative to an overly-complicated conspiracy involving poison, patsies, and an insane golem.
However, there's one far greater threat to the vampire herald's multi-generational breeding schedules, and indeed to his entire eugenics program: none other than Sir Samuel Vimes, himself. Until Guards! Guards!, Dragon King of Arms had surely thought that he'd never have to deal with the Vimes bloodline - a lineage with an undesirable history of deposing royalty, and with too much stubborn rectitude to be manipulated - contaminating the pedigrees of his properly-bred pet nobles. The Ramkin lineage, he'd presumably also judged unfit to preserve and been allowing to dwindle for generations, as Lady Sybil was the last of her family when Vimes met her. Had the two never gotten involved, the Chief Herald would've been content to sit back and watch both bloodlines die out, with Sybil still unmarried and Vimes still a miserable drunk.
But with Vimes's marriage to Sybil, and his subsequent abrupt (unwilling) ascent into the peerage, Dragon King of Arms found himself with a real problem: if the two had a child, that offspring would be heir to the largest fortune in Ankh-Morpork, and an eligible future spouse for many of the noble families he'd been so carefully breeding for centuries. The last thing he'd want would be for the regicidal blood of Old Stoneface (someone he probably knew, and despised, three hundred years earlier; remember how he kept getting Samuel Vimes and Suffer-Not-Injustice conflated during their first meeting?) to contaminate his purebred stock. And simply killing Vimes himself would only incite the wrath of the entire Watch, acting under Carrot's command: Carrot, whose narrative status as the True King and Dashing Hero Dragon is enough of a royalty-booster to recognize, hence someone who would inevitably Get His Man.
A truly good King, a half-werewolf royal heir, a fully-functional Vetinari, were all potential problems that the vampire's scheme would deal with along the way, but it's Vimes himself whom he had to discredit, first by making him look incompetent as Vetinari's protector and second by framing him for the poisonings. Any fringe benefits obtained may have been useful for ensuring that the upper-crust would play their parts correctly, but to Dragon King of Arms they were just the serum atop the corpuscles.
- Except that the reasons for a) not picking Carrot, b) using the candles, were given by Vimes, who'd worked them out. First, the likes of Dragon have caught on that Carrot really would be The Good King and just to all, acting directly against their interests and promoting a kind of meritocracy that they oppose. Nobby, by contrast, would be an easily controlled patsy who'd just sign off on whatever was put in front of him (in theory). Second, arranging an 'accident' for Angua would be exceptionally difficult - werewolves can be killed, yes, but killing them is extremely difficult, and Angua is both a particularly intelligent and badass werewolf. It would be possible to kill her, but making it look like an accident, when her boss is Sam 'I'm a suspicious bastard' Vimes? Much, much more difficult. It would attract the kind of attention the candles were meant to avoid. Third, the candles are an entirely controllable method of modulating Vetinari's state - they can let him get better, or make him worse, depending on what's useful at the time. It's a little abstract, but it's the perfect way to keep him under control (except that he'd figured it out). Fourth, he doesn't really have much of an opinion of Vimes, inwardly dismissing him after their meeting as "a stupid man", one he presumed had uses for Vetinari because "stupid men would do things that the clever wouldn't dare contemplate."