The Missouri State Statute 452.375 addresses the factors the court considers in awarding custody in a divorce
and they are as follows:
(1) The wishes of the child's parents as to custody and the proposed parenting plan submitted by both parties;
(2) The needs of the child for a frequent, continuing and meaningful relationship with both parents and the ability and willingness of parents to actively perform their functions as mother and father for the needs of the child;
(3) The interaction and interrelationship of the child with parents, siblings, and any other person who may significantly affect the child's best interests;
(4) Which parent is more likely to allow the child frequent, continuing and meaningful contact with the other parent; (this factor works in the mother's favor since the dad denied access to the kids)
(5) The child's adjustment to the child's home, school, and community;
(6) The mental and physical health of all individuals involved, including any history of abuse of any individuals involved. If the court finds that a pattern of domestic violence as defined in section 455.010 has occurred, and, if the court also finds that awarding custody to the abusive parent is in the best interest of the child, then the court shall enter written findings of fact and conclusions of law. Custody and visitation rights shall be ordered in a manner that best protects the child and any other child or children for whom the parent has custodial or visitation rights, and the parent or other family or household member who is the victim of domestic violence from any further harm; (this works against the parent you said is verbally and sexually abusive).
(7) The intention of either parent to relocate the principal residence of the child; and
(8) The wishes of a child as to the child's custodian. The fact that a parent sends his or her child or children to a home school, as defined in section 167.031, shall not be the sole factor that a court considers in determining custody of such child or children.
The mother in this case has a strong advantage because she is the primary caretaker and given the young ages of the children, that also tends to favor the mother under the "tender years doctrine" courts lean towards giving custody of younger children to the mother if she is the primary caretaker. When the children get older a court may consider the child's wishes. I hope this helps clarify, please let me know if it does not.
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