msseeker:
B’derech Klal, Chassidish ladies work as parents, which is the best thing that a mother can do, and the husbands work.
If you are a “Yotze min Haklal”, and your Rebba said that you should work, then you should speak to him regarding internet as well. As far as you know, he may have good resons why you SHOULD have internet.
As we always say here, ask your LOR.