The right to custody belongs first to the mother, then her mother however high, then the maternal aunt, then the mother's maternal aunt, the mother's paternal aunt, the paternal grandmother, the father, the sister, the paternal aunt and others, in the order set out in the law (art. 189). A custodian must be of age, sane, trustworthy, and able to raise the child and protect them physically and morally (art. 190).
The mother loses custody if she marries someone who is not a mahram to the child and that husband consummates the marriage (art. 191). Also, if the person entitled to custody stays silent for a year without excuse after learning of the marriage, the right lapses, and claiming ignorance of this rule is no excuse (art. 191).
The right of custody is not lost by waiver; it is only suspended by its impediments and returns when they cease (art. 193). Women's custody of a boy ends at puberty, and of a girl at her marriage and its consummation (art. 194).
This is general legal information, not legal advice. For advice on your specific situation, consult a lawyer licensed in Kuwait.