I'm so sorry. Your mom has what they call "high load" stage 4 metastatic cancer, vs "oligometastatic" stage 4 like my prostate cancer (just one known metastasis, though it did a lot of damage to my spine).
I don't know much about modern breast cancer treatments, but for prostate cancer there are many new treatment options now, even after it spreads like that. None of the treatments is a picnic, though, and many increase the risk of other conditions like heart disease or diabetes.
I was 56 at the time of my diagnosis and mostly healthy (except that the cancer had left me temporarily paraplegic), so we decided to "throw the kitchen sink" at my stage 4 cancer. So far, it's doing the job and I feel I still have a good quality of life as well as quantity. Treating her cancer with "curative intent" could buy her more years as well, but it could also make her sicker, especially if her health already isn't great.
As others have mentioned, there's nothing wrong with choosing palliative (focus on managing symptoms) over curative (focus on fighting the cancer), or vice-versa. This is a decision she'll have to reach after talking with her care team and family.
Best wishes.
I also want to add that "palliative" isn't the same as hospice. Palliative just means that the treatment prioritises reducing pain (even though it might also fight cancer); curative treatment prioritises fighting cancer (even though it might also reduce pain). Hospice is end-of-life care, but even then, many people are discharged alive from hospice because their palliative treatment at the hospice is enough to push the cancer into remission. It's all pretty confusing at first.
It freaked me out when I came home from hospital after 3½ months and homecare made a visit and told me that I was getting palliative care. I called the hospital, and they apologised and explained that the classification is automatic with any kind stage 4 cancer, even though I've been getting curative doses of treatments. My oncologist now tells me that I'm in full remission (with the support of the "forever meds"), though "remission" is another tricky term ...