AA vs KK how to play?

Sat night at G sat on 1 /2,

Im on the button. Player 1 is under the gun and Player 2 is to the right of me. I get dealt pocket kings, Player 1 raises to 10 Quid. Player 2 raises to 45. I make it 90 to go. It goes back to player 1 who pushes 104 all in. player 2 raises all in as well to 500. At this point my stack is 190. Basicaly im getting 3 to 1 to call.

Little background player 1 about 10 hands before this He and i were in a hand and he raised all in about 100 quid with AJos after i raised with to 30 with pocket 10's I folded and he showed his hand.

Player 2 was playing loose but i picked up a read on him. I was postive my read was good.

I figure that player 1 has something like A J AQ AK Maybe AA QQ. Im pretty much priced in to call him any ways its like 10 more to call him which is a no brainer. I figured that i had him beat. Even if he AA i would still end up making 100 quid off of player 2.

From the read i was getting from player 2 i figured he was trying to push me around. He might have pocket aces but i couldn't put him on that hand from my read even though he was representing that hand. So i call and guess what they both had. Pocket AA's both of them. No help from the flop turn or river. And im done for the night.

I figure i made the right choice due to my read on player 2. Player 1 wasn't really in the picture. Im not mad about this, just chalking it up to poker variance. What do you think?