Let's say it is the Challenges Phase. Player A is playing House Stark and Player B is playing House Targaryen. Player A has a Robb Stark [LoW]. Player B ambushes a Flame-Kissed onto Robb Stark. Player A knows that Player B has one Forever Burning in their hand, and thus would like to use a) Robb Stark's ability to name a trait to gain +1 STR or b) Forever Enduring to protect their character. Is it the First player who gets to choose which player is allowed to make a player action when both players want to?

(Also, just to verify, once Player B uses the Forever Burning on Robb Stark, if Player A has not yet used a +STR effect on Robb Stark, it is too late to do so. His STR is 0 and he is killed. Right?)

Actions alternate between players in each window, starting with the first player. Ambushing Flame-Kissed on Robb is an action, so it's Stark's turn to take one (assuming no other players). Have a look at the FAQ for detailed flowcharts.