First, I am sorry to hear of your mother's diagnosis.
It's hard to say how long as everyone is different. My mom was diagnosed with extensive stage small cell lung cancer in April 2015 (lung-primary which had spread to liver, lymph nodes and bones by time of diagnosis). Did chemo and went into remission in August 2015. In January 2016 had a TIA (mini stroke) and found 50+ tumors in her brain. Did Whole Brain Radiation Therapy and killed them all.
In April 2016, cancer had returned to her liver. Chemo started again. In June it was stable...hadn't grown or shrunk. Today, Aug. 23, 2016 scan showed the liver tumors had grown and new ones had formed, as well as one in her lung...all while being on chemo.
So Dr ordering 3rd line of chemo drug (my mom has refused clinical trials all along) and that starts next week. Dr worried about the liver function because if it shuts down, she has to stop chemo and there is no other option at that point.
She's weathered all chemo to date well...only lost hair and hearing loss, but no nausea or vomiting or weight loss or anything else.
We are essentially in pallative stage...there is no cure...but trying to give her as many days left as possible.
The best advice is live in the moment with her and spend whatever time you can with her as much as you can.