"Mum" is
capitalized here because it's acting as a name.
There was ice cream that Mum had made herself. Betty said her mum made better ice cream, but we knew she was lying because she didn't have a mum - her mum ran off with the ice man last year. Soon we heard Mum calling us to come eat the cookies she'd made to go with the ice cream. "Mum," we said, "this is delicious, but please stop showing off. You're making Betty feel bad."