I am so sorry to hear of your Mom's diagnosis. I'm afraid, dear, that this may just be too much for you to handle on your own. Given your own personal medical history, it may be wise to seek out some help from social services in your area. You say your brother and sister don't "seem" to want to do it. Well, you just never know unless you ask. You need to be honest with them, and tell them EXACTLY what you've told us here. Surely they must realize that your own situation is fragile and that they need to step up to the plate.
Check out your mom's health insurance and see if there is a hospice she may go to. I don't know what her prognosis is, or staging, or even the type of lung cancer she has, so it's hard to help you with suggesting hospice. But, if she is in the end stages, hospice should be able to help. Is she getting treatment? Or is she past any treatment options?
I worry about you though. You've been institutionalized once. Do you really want to put yourself in the position to jeopordize your sobriety? Do you really want to put your health at risk? You may want to help with your mom, but you can do that if she is in hospice, or at a sibblings home. But at this point it seem un-wise for you to take this on by yourself in your own home. You have 2 children to think of, and a job to keep. I personally, in your possition would not risk my mental health., You must think of your kids, do they need to see you go down the path you've already traveled?
I hope you find help from someone, or hospice, or social services. To me the risk far outweighs your desire to be there for your mom in your own home.
Take care dear, I'll keep you in my prayers for God to guide you to the wisest choice, and send help for your Mom.
Byrd