So what are the main ideas behind family ties with Nichiren?

Bodhisattva families, collective efforts for the great Buddha work of kosen rufu , the more the merrier.

they why the married prctitioners would make their prayer for the arrival of 'fortune child ' to their family - bodhisattvas of the earth to be reborn here for their work

'Drink sake only at home with your wife, and chant Nam-myoho-renge-kyo.'

Gosho: Happiness in This World

Hi, LD -

Nichiren was a man of his times in many ways. Japanese society was strongly influenced by Confucian ideals, and Nichiren absorbed these Confucian ideals and incorporated them into many of his teachings.

He often talks about being filial, about duty to parents and so on. He talks about hell being in the heart of a man who despises his parents. I don't have the reference material in front of me, but can get it if necessary.