Which is more preferable: searching for a committed wife, or marrying the daughter of one's paternal uncle who admits to her disobedience and does not wear the hijab? And what is safer for one's religion and greater in reward?

If your female cousin is righteous, and by her not wearing a hijab you mean she does not cover her face but covers the rest of her body, then we hope you will be rewarded for marrying her and helping her maintain her chastity, especially if you strongly believe that she will cover her face after marriage, as this involves kindness and maintaining kinship ties. However, if by not wearing a hijab you mean she does not cover her head or similar, then we do not advise you to marry her in that state. It is better to seek a woman of religion and character, acting upon the Prophet’s (peace be upon him) recommendation: "Then marry the one who is religious, and you will be successful." Marrying a woman who is not religious in the hope that she will become righteous after marriage is an unsafe path.