She got kicked out of her dad's place for seducing his GF's adult-age son (red flag, I know).
That's really weird phrasing; seems like it assigns blame 100% to her for something that 1) seems like something that really takes two people to do and 2) seems like something that only the people involved would know the truth of. Just...weird.
As for the rest, it boils down to her saying she has various serious medical issues, and you not believing a word of it. Could she be lazy and just making everything up? Yeah. Could she be at the end of her tether and in the process of crashing? Yes.
I mean, you say:
I am the only member of the marriage who can physically work as my wife has had medical issues for the last 2 years that have prevented her from working.
So clearly you accept the concept of someone being unable to work. And your SiL is apparently saying that she has medical issues which are so bad that she "needs" to stop working, and has suggested that it's a matter of life and death. Is that true?
I think, basically, you need to decide:
Keep in mind, that while going hungry might teach her some valuable life lessons, it's also possible that she'll just end turning to drugs or prostitution. It's not particularly unlikely that she'll end up raped. Or murdered. Or at least needing to trade sex for survival. But hey, she's an adult. ...and family. You may need to figure out how to balance those versus you (and your wife's) needs.
(Not sure