@Willy Matadi ameshakwambia. Custody a child of tender years [like your 3 year old] SHOULD be with the Mother. That is the law. Kupata custody itakuwa NGUMU KABISA!
And no, the fact that she abandoned another child, who is not yours and whose custody is not presently in contention, is not a sufficient ground for you to have sole custody. If you dare raise that in court, the magistrate will laugh you out of town then dismiss your suit for custody, WITH COSTS.