Let me try and help. Breast cancer is breast cancer, regardless of where it spreads. If it spreads to the liver, it is still breast cancer, but it is called metastatic breast cancer. They can tell by looking at cells and determining what kind of cancer it is, through a biopsy.
Breast cancer is not always easy to detect. The mammography, US and MRI were ways to look at the breast tissue to detect the lesion, or tumor. Not everything is detectable, unfortunately. When breast cancer spreads out of the breast, the first place it is most likely to get detected in in the lymph nodes. They filter the cancer (and infections or other impurities) before it goes elsewhere. We have lymph nodes all over our bodies...behind the knees, groin, clavicle area....
Some breast cancers are not easily detected by tests, such as lobular breast cancer. Others are seen right away. My tumor was 2.5 cm, and you could not see it on the mammogram.
You asked about checking out the breast, the tests you mentioned are the ways in which they checked out the breast. They may have scanned other organs to look for cancer or done blood tests. And yes, if they cannot locate the cancer in the breast, but it is definitely breast cancer in the lymph nodes, then they will probably want to remove the breast.
Survival is very high, and usually depends on several factors. More node involvement may mean higher chance for recurrance. Nothing is a guarantee though...some with tiny tumors have it spread, and others with large tumors never have to deal with it again.
I would encourage you to go with your mom to appointments and ask these good questions, then get a 2nd opinion. A major hospital at a university is a great place to start.