There is nothing you need to do other than keep the mom's cup filled with clean water. Just for the future, the cells that line the cup are specialized for the uptake of water and fertilizer. If they are damaged, it can compromise the plant. I'm not sure I would use anything like alcohol on the cup of a bromeliad. Those cells are delicate.
No, just leave the pup be. It is actually cannabalizing the other plant to help it grow. That is one reason she is dying. She will get unsightly, but resist the urge to remove her.
You shouldn't try and separate the pup until its at least 1/2-2/3 the size of the mother. The mother may just desiccate before that happens, if it does its okay to remove the spent leaves.
Its an exercise in patience
