Sentence:  If a dad is commuting to the city to New York and goes to New York on the seven o'clock train and comes home on the seven o'clock at night train, then he is a <WSD>weekend dad</WSD>; [he] is not really involved as the primary parent. 
Meaning of the word marked with <WSD> tags:  A custodial father whose time with his child/children is limited mainly to weekends.