Here are the mitigating factors I found that look to be pertinent to a defendant's parents/family:
6.8.9 OTHER STATUTORY MITIGATING FACTORS
(1) Family background
Generally, family background problems can be considered as a mitigating circumstance.604 Usually this mitigating circumstance becomes an issue worthy of significant weight when the defendant has a “troubled background with a family history of instability, poverty or abuse.”605 While it is unclear how much weight a “good family background” should be given, it is error to completely reject this mitigator as worthy of no weight.606
(5) Mental problems that do not qualify under other statutory mitigating circumstances
This mitigating circumstance covers a variety of different situations. It has been applied in a case where a psychologist referred to the defendant as an “emotional cripple” who was brought up in a negative family setting.617 It applies in a case involving posttraumatic stress disorder as a result of extended sexual abuse by the defendant’s stepfather.618 (Both are one word) Usually, the testimony or other evidence establishing this mitigating circumstance does not rise to the level of "extreme" mental or emotional disturbance, or "substantial" incapacity. It is something less than “extreme” or “substantial.” However, the evidence must still be considered by the jury and the judge as a mitigating circumstance. The trial judge must allow the evidence to be presented, and it must be considered in the sentencing order.619 In Stewart v. State,620 the Court stated that it was not error for the judge to find the statutory mental mitigators did not exist, but it was error for the judge not to find the same evidence as nonstatutory mitigation. Depending upon the facts, it would generally be appropriate to give less weight to mental problems that do not rise to the level of “extreme” or “substantial.”
(6) Abuse of defendant by parents (physical, mental, or sexual)
It is well established that a disadvantaged childhood, abusive parents, and lack of education and training, are mitigating in nature. Although in some cases family background and personal history may be given little weight, such evidence must be considered by the Court and discussed in the sentencing order. Mitigating evidence is not limited to the facts surrounding the crime but can be anything in the life of a defendant that might militate against the appropriateness of the death penalty for that defendant.621 The nonstatutory mitigator of defendant's abusive childhood should
not be rejected, even if the defendant demonstrated good behavior in adult life.622
6.9.7 THE DEFENDANT HAS THE SUPPORT OF FRIENDS AND FAMILY
Evidence of positive “family relationships and the support (the defendant) provided his family are admissible as nonstatutory mitigation.”681 It is error not to consider this mitigation, but the error may be harmless if these factors are otherwise considered.682 The reverse, negative family relations such as abandonment as a child, are not always mitigating.683