Wow. This woman has clearly spent a lifetime cultivating her co-dependency and it sounds like her "friends and family" have done nothing but enable it.
Listen closely, K., because this is important...
She.is.not.your.problem.
Now I know that sounds heartless, but you have to understand something. She is a grown adult that has not matured past adolescence. She cannot handle her own finances, her own housing, or any of her personal business. I'm honestly surprised she manages to wipe her own rear-end.
Surely you've asked yourself why she is the way she is? Well, the answer is simple...nobody has ever forced her to grow up. It sounds like you're just one in a long line of family members that has sought to help this woman, so what on Earth makes you think that YOU can somehow teach her how to take care of herself and move out into the world voluntarily?
Let's be clear about one thing. This is America, not some third-world country. Nobody starves to death in America (unless it's by choice). Nobody lives on the streets (unless it's by choice.) Does she have too many bills and not enough money? It's called Bankruptcy. Do her medical problems keep her from earning a proper income? It's called Disability. Can she not afford her own place on $300? They're called ROOMMATES! Or even housing assistance, if she's willing to apply. Does her lack of education keep her from earning a decent income? It's called College and the government will pay for all of it in the form of low interest student loans (that do NOT depend on your credit score and are deferred while you're in school) and even a wonderful thing called a Pell Grant.
The point is, K., that this woman clearly has options. She is choosing to live the way she does because it's just how she is. Some people are like that. They use other people until they wear out their welcome and then move onto the next victim. She will NEVER change, not as long as you continue to enable her behavior. What she needs is tough love. Unfortunately, even if you decide to give that to her and kick her out, there will probably be another family member that will cave in to her. But again, that's not your problem.
Your priorities are with your husband and your boys. Period. And there is NO way that you can continue to be a good wife and mother with this woman bleeding you dry...financially, physically and emotionally. It is not a healthy situation for anyone, including her.
I think you know what you have to do, but you're just too dang tenderhearted to do it. Well then, don't do it for yourself...do it for your family. And if validation and support are what you need, then you're sure to get it here. Only a complete nut-job would tell you to continue supporting this leech.
It doesn't really matter how you do it, just so long as you get it done. Tell her the truth, or a version of it...that you can no longer afford to have her live with you and you need her to leave. Surely someone with her background can understand financial difficulties. If it makes you feel better, tell her that you'll always be there to provide emotional support and advice...just not room and board.
I'm sure it's not the first time she's been sent packing so please don't worry about her. People like that always manage to land on their feet...usually in someone else's home. And please don't feel like a bad person, K.. You have already done more than most people would ever have considered. You are obviously a kind and compassionate individual...just the type that people like your "relative" love to take advantage of. If you're into doing good deeds, go volunteer with a charity. Go help an elderly person cross the street. Heck, since you clearly have a lot of love to give and a desire to care for others, you could even consider becoming a foster parent.
But don't waste your kindness on being this woman's doormat. Because that's exactly what it is...a waste.
Good luck to you.