Either parent may have the custody of the person and care of the education of the minor, if the court, at the time of appointing a guardian of the minor, deems the parent to be competent and suitable for that purpose. If the court deems a parent incompetent or unsuitable, it shall direct accordingly in the letters of guardianship. In its discretion, at any time during the continuance of the guardianship, the court may change the custody of a minor, upon notice and after hearing, if the court finds the person having custody incompetent or unsuitable. (Amended 1985, No. 144 (Adj. Sess.), § 122.)