@Boartank
Regent is the one who would be in charge, when the emperor is incapable or unavailable. Either a regent or regency council would usually be put in charge for monarchs that aren't of age, but they tend to be way older than the then minor monarch.
I'm expecting Vice Emperor to be something like the Deputy Ruler, or the role a Crown Prince(ss) or Empress / Emperor might've had, had they married the imperial family for political reasons.
Basically, Vice Emperor might sound very odd, but having a way more minor child as a Regent would be insane, and he can't qualify / wouldn't be accepted as a minister / crown heir or imperial spouse, and even if he was suddenly make a duke, marquis, margrave or similar higher nobility or an advisor, people wouldn't know what to make of him (they probably don't do it anyway right now, but hey)