Their father indeed appeared at the end of the second season (see below).

Not only that, but the father appears to believe he actually has his son's best interests at heart.

Her father had not appeared at the table, much to the children's relief.

I had nearly got to the front door when Father appeared at the top of the stairs.

He was happy to see that his father appeared not to have noticed.

His father then appeared to give him a dressing down.

The director's father also appears in the film, which opens today.

But then the boy's father appeared, and "everyone was so happy to see him alive."

She kept the toddler for about a week, until the child's father appeared at her door.

His father appears only in the first and the last two episodes of the second series.