How to avoid being stuck in the middle?

You can support both. I would say to the daughter that it's is her life and there is much she can do that is not too invasive but at the end of the day it is her choice. No one wants to lose a parent and its possible purely natural life will end before the cancer causes issues.  Often at 88 it could be a very slow growing estrogen cancer. AI's can be all the treatment. ..or just lumpectomy and radio. These days Drs take age into account and think of quality of life. As to the lady with the lump,  I guess just discussing the path if no treatment is important. Nobody wishes their last years to be filled  with lots of pain or loss of independence  and that probably is something she needs to consider when she makes her decision.

 I had a friend I met during chemo around 80. He had prostate cancer for over 10 years. Hormone therapy was initially all he was treated with. Eventually he did have chemo...and did really well. He just thought...what the hell...I've still got more living to do. We did an exercise program together. Kath x