On Encouragement of Abuse by Mother: CAUTION: some readers, especially survivors of sexual abuse, may find Gardner's remarks deeply disturbing. Indeed, we all should.

“In some cases the abuse was actually encouraged (overtly or covertly) by the mother in order to use the child as a substitute object for the father’s sexual gratification.  Such mothers view sexual encounters as odious, and the child is used as a convenient replacement – protecting the mother thereby from exposure to the noxious act.”
RICHARD A. GARDNER, THE PARENTAL ALIENATION SYNDROME AND THE DIFFERENTIATION BETWEEN FABRICATED AND GENUINE CHILD SEX ABUSE  122 (1987).
“Sometimes, mothers who were sexually abused as children may have set up a situation to increase the likelihood that the father will abuse the child.  They may do this as a way of mastering their own abuse trauma.  They may secretly and/or unconsciously hope that the child’s resistance or successful working through will vicariously enable them to do the same for themselves.  Or, they may have responded to the abuse by frigidity or sexual unresponsivity and use the child as a substitute source of satisfaction for their husbands.”
RICHARD A. GARDNER, THE PARENTAL ALIENATION SYNDROME AND THE DIFFERENTIATION BETWEEN FABRICATED AND GENUINE CHILD SEX ABUSE  130 (1987).
 “Sexual abuse of some girls by their fathers is sometimes consciously or unconsciously sanctioned by their mothers.”
RICHARD A. GARDNER, THE PARENTAL ALIENATION SYNDROME AND THE DIFFERENTIATION BETWEEN FABRICATED AND GENUINE CHILD SEX ABUSE  194 (1987).
“Sometimes the mother’s abuse has resulted in sexual inhibition problems, resulting in their viewing sex as disgusting.  They may then facilitate (consciously or unconsciously) their children serving as sexual substitutes in order to protect themselves from involvement in sexual acts.” 
RICHARD A. GARDNER, TRUE AND FALSE ALLEGATIONS OF CHILD SEX ABUSE 185 (1992).
 “[A] mother who is sexually inhibited may view sexual encounters with loathing.  Consciously or unconsciously she facilitates the father’s turning his sexual attentions to her daughter in order to ‘get him off her back’ (or ‘front,’ as the case may be).  In this way, she avoids involving herself in the ‘disgusting’ activities and yet allows ‘the beast’ to gratify his primitive needs and keeps him ‘tamed’ and out of ‘trouble.’” 
RICHARD A. GARDNER, SEX ABUSE HYSTERIA: THE SALEM WITCH TRIALS REVISITED 36 (1991).
http://www.stopfamilyviolence.org/info/custody-abuse/parental-alienation/quotes-by-richard-gardner