Hrqls: In matches we use a rule called the crawford rule, which says that doubling isn't allowed in the first game after one player has reached one-away (2 in a match to 3, 4 in a match to 5, etc.). After that game doubling is allowed again.
In your 1-2 game, your opponent should drop if you are a favourite, since by dropping he would be 50-50 to win the game from the score 2-2 (assuming equal strength).