This may help. Taken from Texas Express rules posted at
http://www.angelofbilliards.com/resources/TexasExpress9-Ball-Rules.pdf
5.2: Legal Frozen Shot
When the cue ball and lowest numbered ball are frozen together, the player may shoot directly through the cue ball with a normal stroke (the normal momentary time commensurate with a stroked shot). The frozen balls must be declared and the opponent must acknowledge the declaration prior to the shot. If the player shoots without declaring and receiving acknowledgement, the shot will be considered an illegal push shot.
5.3: Illegal Push Shot and Double Hit
When the cue ball and the lowest numbered ball are barely separated, the player may not shoot directly through the shot if the action causes a push shot or a double hit. (The players should have the tournament director observe any shot where the cue ball and lowest numbered ball are barely separated.) There is no requirement that the cue stick be elevated in an attempt to eliminate the possibility of a push shot or double hit. Refer to rule 5.4 (Push Shot Definition) and rule 5.5 (Double Hit Definition) for clarification.
5.4: Push Shot Definition
A push shot may occur when the action of shooting causes the cue ball and the numbered ball being struck by the cue ball to travel at generally the same speed and distance. A normal stroke is defined by the action of the cue tip striking and not pushing the cue ball. A normal stroke is determined by the time and distance the tip remains on the cue ball, commensurate with a normally executed shot. A push shot constitutes a cue ball- in-hand foul.
5.5: Double Hit Definition
A double hit occurs when the action of shooting causes the cue ball to be struck twice (or more) by the cue tip during a single shot. A double hit constitutes a cue ball-in- hand foul. A double hit is usually caused by the cue ball rebounding off the object ball being struck, causing the cue ball to hit the cue stick tip (or ferrule or shaft) more than once.
