I can think of one reason, and only one, why Charlie would switch sides:
If he thinks it could get him an Arkentool (or more than one.)
I doubt the Arkenhammer is just going to be up for grabs when Stanley's croaked, at least as things are now; the alliance must have factored its disposition into their plans (after all, if they win, it's going to be the most valuable piece of loot by several orders of magnitude.)
But if Charlie thinks that he has an even decent chance of winning and beating either Stanley or Ansom (much less both) from a position that would let him grab their Arkentool, I suspect he would leap at it, reputation or no. Arkentools are the McGuffins. Heck, there are only four known arkentools total -- if Charlie could stab Ansom in the back and grab the Arkenpliers while simultaneously stabbing Vinnie/Wanda in the back, then killing Stanley himself to take the Arkenhammer, he would easily be the most powerful faction in the world.
(This assumes, though, he can attune to them, which he might be confident of doing after his presumed success with the Arkendish... or not. It is also possible that the Arkendish lets him determine who the other tools will attune to, which could explain his attention to Parson, but that is purely speculative on several levels.)
In any case, though, if he thinks the Arkenhammer at least will attune to him, his logical strategy is this: Send more Archons than expected, splatter Vinnie and Jillian when the fight with Stanley begins, splatter Stanley and grab the Arkenhammer while killing as few dragons as possible, then grab the remaining dragons and take Ansom by surprise while he attacks the now-neutral city.