You sound like me when I was young and felt so stuck. Yes, you can work yourself out of this swamp.
Can your wife work nights while the kids are asleep? Then you won't need the aunt living with you to take care of the kids.
Can you start a business on the side and have your wife run it from home while you work?
Can you take some on-line classes to help you with your job skills and resume? There are cheap classes and free materials available for the asking...
Can you buy a small house with owner-carry financing? That gives you the chance to make the aunt very uncomfortable since she wouldn't have as much space. It sounds like the only way out of having her live with you (without fighting your wife), is to get her to decide to move on. Fish and company get old and smelly in 3 days. The aunt is definitely over her limit. You could sell the idea to your wife by reducing your monthly rent "nut" by having a lower payment and the benefits of home ownership. And that would give you a break. Then you could take monthly windfall and use it help you make a career move...
Another way to solve the "aunt problem", is take a job far, far away from your present home. I bet she won't wanna make that move. Then you may "have-to" have a smaller living space to make the transition.
Look at other careers and see what else is available. You might not need your suit anymore. There are blue collar training programs that pay more than you are making.
AS a note: I think that your wife is using her aunt as her "security blanket". She's terrified of being on her own and having to grow up. This is a common problem with young people who aren't used to making grown-up decisions. It's easier for her to have someone to rely on. And the aunt is using you guys, as a couple, to not have to make it on her own either. You are all co-dependent. Confronting your wife, kicking out the aunt and causing a fight will be ugly and it won't work. You need help sorting it all out. This is a human problem -- not a real estate investing problem...