Hello English,
You are correct about Player 2's hand being live. A penalty should be enforced, however, he must win the pot. Circumstances can call for different penalties. A good example is if a player intentionally shows cards, as opposed to a player not realising there are other players yet to act.
It is a violation of proper etiquette but (in my opinion), a player in for all bets that tables his hand, should never have his hand ruled dead.