(Not a women, but Swede that have lived in US).
Sweden (and nordic countries in general) is regarded as most gender equal places in the world. Comparing with the US, I would say that the oportunities and safty for women is much better. (But it also depends on which state you compair to).
That said, Sweden can culturaly be hard to integrate into. It is not easy for grown-ups to build a new life and find new social connections. Your daughter would probably not have any problems, but you and your husband might. And it is not easy to find qualified work without speaking Swedish, unless you have some special skills. (But I know people from US and Canada that have made the transition).