What was the Song Dynasty like for the women? Was it illegal for them to work outside of their homes?

I don't think so. The women of the Song Dynasty have high social positions compared with the women of other dynasties. They are even richer than those of the Tang Dynasty. Their main jobs are silkworm breeding and spinning and weaving. Some of them open tea houses or become street vendors.

No it wasn't illegal.

well it depends where they lived if they were from rich families they didn't exactly need to do work since it was done for them but instead they would bind their feet. but the people who lived in the country side they were allowed to work on the farm. they were actually kind of forced

no it was not illegal for them to work outside there homes but they did have some jobs with restrictions of gender type. :)