Can I choose difference house card without discard two power tokens?
I think the correct way to read this would be:


Discard 2 power tokens immediately
Discard Aeron Damphair
If able, choose a different house card from your hand.


Please note that step 2 can't be completed without step 1. Similarly step 3 can't be executed without steps 1 and 2.

This would mean that your friend is wrong as you have to discard 2 power tokens to even make it to step 3. 

You must play a new house card if you have one in your hand and you've discarded your 2 power tokens and Aeron Damphair. The only time you shouldn't play a new house card is if there isn't one in your hand.

The 2 power tokens that need to be discarded also seem non-negotiable to me. If they don't have 2 power tokens to discard, they can't activate this card (unless another card says otherwise, but that's a little off topic).