It's this example sentence that explains 比较……的是 better than the lesson notes.

「比较辣的是这个火锅」 means "The (rather) spicy one is this hot pot", and 「比较难吃的是他们的饺子」 means "the (rather) nasty ones are their dumplings"

The English in the lesson notes is not right.

Mom is sad. 妈妈很伤心。

My mom is older.

"My mother is the older one." Is acceptable i think.

"My mother is the older one."

"my mother is older" should be accepted