I think inequality is negatively related to true well being. This relation is partially direct, and more importantly emerges as almost all social problems, be they drug use, crime, high school dropout rate, or teen pregnancy, create income inequality. As a side note this second effect leads to an endless spurious correlations as the left claims that it is income differences that is causing crime or drug use, and demand income transfers as useless remedy for deeper social pathologies.
Self-reported happiness is mainly a ratio of expectations and outcome, not an absolute measure of well-being. That is probably why the relative self-reported happiness of women has fallen, while their status has increased. They are better off, but their expectations on life have risen even faster than their status in society, so their self-reported happiness has declined.
Furthermore, reported happiness seems to depend on culture. Latin Americans report high levels of happiness, whereas for example the French give low scores (perhaps the French believe that claiming to be happy about life is low-brow). My best guess is that this odd positive relationship between inequality and happiness is created by chance, as cultural areas with high inequality (Latin America, Arab countries) tend to give high answers on self-reported happiness.
I simply cannot accept that El Salvador is better off than in France, South Africa better than off than Hong Kong, or Guatemala better off than Germany. Revealed preferences show that per capita GDP dominates indices of self-reported happiness. When people get to choose they try to move from El Salvador to the US and from Nigeria to France, as GDP predicts, but opposed to what self-reported happiness would predict.
Those on the left, who (having lost the income creating battle) now want to replace objective measures such as GDP with subjective measures such as self-reported happiness should keep these problems in mind.