How do you reach the conclusion that people "want" to have children in the sense of that link?

I am skeptical of giving much weight to "wants" in the sense of that link, but I don't think children are such a want. I do think that there is another relevant distinction in happiness research, between asking people "How do you feel right now?" vs "How satisfied are you with your life?" Childcare is very bad on the "like" scale, but a child produces much pride and life satisfaction.