Song Hong was indeed Song Chongjin's biological father, and Song Chongjin's mother was named Qi Huan, the daughter of the Hanlin Scholar Qi during the previous Emperor's reign.
If the Song Family had retained the glory from when Duke Weiguo founded the country, the two families would have certainly kept to their own affairs, never interfering with each other.
However, Song Hong's grandfather had sided with the wrong faction before the previous Emperor ascended the throne, so after his ascent, Duke Weiguo became obediently low-profile.
Every dynasty, upon its establishment, would foster the arts and devalue military accomplishments.
After dimming down their presence, the Song Family aimed to cultivate their children in the ways of scholars, thus deliberately seeking closeness with the Qi Family.
Song Hong and Qi Huan shared a childhood friendship, their relationship being particularly affectionate.