Yes, you can apply for citizenship for your wife since you obtained citizenship of St. Kitts and Nevis from your parents' application as a dependent.
Can my wife get St. Kitts citizenship if I am a dependent of my parents’ CBI application?
I obtained citizenship of St. Kitts and Nevis through my parents’ CBI application. I want to get married with a girl from my home country. Can I apply for St. Kitts citizenship for her?