How should one deal with a wife who does not wear the niqab, and cites opinions from figures such as Al-Qaradawi and Al-Ghazali regarding its non-obligation, and is the husband sinful for her non-adherence to the Sharia-compliant hijab?

If the wife's clothing fulfills the conditions of the Sharia-compliant hijab, and the issue is restricted to covering her face, then there is no blame upon you if you are patient with her and deal with her gently, while continuously advising her. This is because the issue of covering the face is among the well-regarded matters of scholarly disagreement. The preferred view among all is covering the face, and those who said it is not obligatory almost agreed on its obligation when there is a fear of fitna (temptation/strife) by the woman or upon her. If the husband commands his wife to cover her face, then it is obligatory for her to obey him, even if she does not believe in its inherent obligation.