How can you reliably deny the presence of an experience of another if you cannot prove that experience in yourself?
With the duplicate mother problem, if you cannot tell then there is no reason to believe that it is not a being of equivalent nature. That is not the same as identity, for a layman approach to that viewpoint, see Star Trek: TNG, Season 6, Episode 24. A duplicate Will Riker is created but is still a distinct entity (and one might argue, more original since has been transported one fewer times). Acting the same as is not the same as being the same entity. Nevertheless it has no bearing on whether the duplicate is a valid entity in its own right.
You feel like I'm not living in the real world, but I am the one asking what basis we have for knowing things. You are relying on the presumption that the world reflects what you believe it to be. Epistemology is all about idetifying exactly how much we know about the world.
It follows from that that you cannot exclude something that appears to have a property if you cannot prove it doesn't or even prove it if it does.