Sounds like you're having to be the strong one in the household right now, your sister is too depressed and your sister in law is too stressed from being the wage earner. Keeping a log of the jobs you apply for is a good idea, you are trying your best and that is all you can do with that one.

Can you all come together and try and talk openly without starting WW3? It would be better to have an open discussion than the toxic sniping. Otherwise could you just say, "you know what, this conversation is getting us nowhere" and refuse to be drawn into the grumbling and griping?

It is not easy being the strong one and I frequently want to run away from my responsibilities, it would be so good to be free. Unfortunately, I like my warm bed and home comforts too much.