Fat-Dart wrote:
S. Touching Balls
1. GENERAL
a) If the Cue Ball is touching an Object Ball, the player is obliged to "Play Away" from that Object Ball at an angle of more than 90 degrees. (That is, play the shot without causing the Cue Ball to make any initial further contact with that Object Ball)
b.) If, when playing away from a touching ball, the touching ball rocks or moves without being contacted further, but simply because the Cue Ball is no longer there, no penalty will apply.
2. Playing away from two or more touching Object Balls:- If any of the touching Object Balls are of the player's Colour, the player will be deemed to have played away if the player plays away from any one of the touching balls of the player's Colour. That is, the player may play into any of the other touching balls. The player needs then to only pot a ball or cause any ball to strike a cushion to fulfil the requirements of a Legal Shot.

If the cue ball is touching the opponent ball(s), then you have to play away regardless, as any further contact would be a foul, as you obviously have to hit your own colour, not theirs. In the scenario you mention, in contact with yours and theirs, then it's deemed that you have already hit yours, hence you can 'play through' their ball. Same with the black involved, unless you're on the black of course.
If the balls are in such a position that you can't play away from them, then you have no option but to play a foul...

W. Impossible Shot
A situation may arise during a frame where it is impossible for a player to play a shot without fouling. In such a situation the player has no other option but to commit a foul.