Is a raise allowed here? Interesting hand scenario

[PantsOnFire]

I can easily you show you how wrong your scenario is.

Say for simplicity there are three players with cards. You limp for $2, Player 2 raises to $15 and Player 3 folds. It's now back to you. Can you raise? Of course you can, that's what you were hoping for. It's in all the poker books. Limp with AA, wait for a raise behind you and then come over the top. It's a classic trap. (Let's just forget strategy right now about using this play we're discussing rules here).

Alright, let's go through a different betting sequence. You limp for $2. Player 2 raises to $15, Player 3 calls $15. Now back to you, can you raise? Yes. Say player 3 raised it to $50. Can you raise? Yes. Say Player 3 had only $20 and pushed it all in (like your scenario). Tell me how this now prevents Player 1 from raising? It defies common sense.

Edit: Stupid explanation #2. Player 3 has $20 but for some reason he just calls the $15 raise now allowing Player 1 to raise all-in and Player 3 now puts his final $5 into the pot.