Props to Player 2 - s/he gets it!
Player 1 doesn't, really: that person is gaming the DM. Or making a joke, hard to tell in print.
Were I the DM, I'd probably replace your "Me:" line above with
Me: "Good question, Player 2."
= [if the party has a Cleric or other divine agent] "Player 3, you're a Cleric - you recognize this sort of place to be just the sort of prime undead breeding ground your trainers warned you about." (then let Player 3 take it from there)
= [if no Cleric or other divine agent present] "Each of you, roll a d20 to give me a general idea of how much lore you've heard regarding undead, what they are, and how to deal with them." (then provide exposition based on the rolls)
That said, what you're doing obviously works for you and your crew so no worries!
Lanefan