Don't be delicate about it - be honest.
I lost 90% of my hair in chemo 2 years ago. I had a 2 year-old and an infant. I wore a wig professionally (which I hated) and preferred to be myself at home. I'd wear hats in public or my wig if I was really concerned.
Don't worry about your girls. Worry about your mom. Losing your hair is devastating, and she may not get it back with the radiation treatments. Somehow, the angst of having cancer gets filtered into our hair. Some women go bald and can be comfortable with it. I never lost all my dark, thick hair. I looked awful. But, I'd come home from work, take my wig off (my 2 year old told me he liked me better without it), and I'd go outside where all the kids in the neighborhood were playing. Somehow, I thought putting a headband on made it look better. It didn't but, it made me feel better about it.
All the kids knew the truth. I was losing my hair because I had cancer and the drugs made my hair fall out. I didn't mind answering questions. But, there weren't any. No one cared - not the 5 year-olds, not the 8 year-olds, not the 2 year-olds. Apparently, I was the only one.
Miracles do happen. Don't be afraid to ask for other opinions or to question the doctors. They expect your mom to want to get the best possible treatment.