What happens if I pocket both my own coin and my opponent's while covering the Queen?
Under normal circumstances, you count as having covered the Queen, but your opponent has a coin pocketed for free and your turn ends.

If the Striker was pocketed with it, you would pay the penalty for pocketing the Striker and then try to cover it again. However, since you pocketed the opponent's coin, you can't take another turn, so the Queen is put back on the board.

If it was one player's last coin, that player wins.

If it was both players' last coin, you win. If the Striker was pocketed with it, you lose.