Can a mother gain full custody of a child despite her having suicidal tendencies? Got proof from both my parents and aunt

I assume by "full custody" you mean an award of most or all parenting time to the mother. A parent's mental health is certainly a relevant factor in a court's decision in awarding physical custody of children.  Usually, the court would need evidence from a mental health professional as to the parent's mental fitness, not just the testimony of relatives of each of the parents--especially since relatives often are biased for or against one of the parents.  Significant facts for the Court to consider would be the severity of the "suicidal tendencies", whether there have been recent suicide attempts, what mental health treatment the mother is receiving, and, most important, the opinion of a mental health professional as to the likelihood that the mother will continue to have mental health problems that currently affect her ability to safely care for the children and herself, or are likely to affect those abilities in the future.