I don't think Eunjung's mother runs Cafenne anymore. Word is the shop changed ownership this year.
Plus it would be difficult to manage running a coffee shop in Seoul and a restaurant in Gangneung simultaneously.
One thing about this, Eunjung says "my parents are starting anew".
She rarely mentions her parents as a couple.
When she speaks of them, it's usually about her mom or how she hasn't seen her dad in years so it doesn't sound like they've been living together.
For both of them to be running this restaurant is probably very happy news for the Ham family so it makes sense that Eunjung would be particularly excited.