The rules, in this case are pretty clear. The spell never mentions mirrors or reflections, it “summons illusory duplicates." Spell names aren’t indicative of their mechanical effect. See Chill Touch.
There’s also vampire wizard statblock that has Mirror Image on its spell list.
It would be funny if the spell just failed though.
...All of this is pretty sketchy though, it's definitely pushing the limits of what these spells or abilities are intended for, and "having your image move around inside you perfectly so nobody notices" would require an extreme level of control that I imagine most, if not all casters wouldn't have.
If we're trying to design an NPC vampire to foil the mirror check, it's probably better to have them use a custom spell or magic item that's explicitly for this purpose than to try and repurpose an existing spell to do it. "This amulet creates an illusory duplicate of you that fills the same space as your body. When you turn invisible, the illusion remains visible and moves in a random direction away from you" for example.
This approach has a lot of advantages I think.
There is a spell for these types of shenanigans and it's called Mislead