For the most part, Trygve’s relationship with his parents was fairly conventional, while that with his brother was constantly strained. Hadrian was Birkir’s first son from an affair he had with Livia Pius, a woman in Imperial City. When he was made aware of his son’s existence, Birkir settled in Imperial City to help raise his son although he never married Livia. She died when Hadrian was eight and, having no family there, Birkir moved them back to Falkreath.
Hadrian was miserable in Falkreath. The children teased him relentlessly due to his Imperial name and small size. His grandfather, Olvar, was not terribly kind to him either, disappointed that his only grandson so far was an Imperial with a terrible milk-drinking Colovian name. After several months of being tormented by the local children, he complained to his grandfather who said that he was in Skyrim and he needed a Nord name. For a couple of days they tried to Nordicize his name to no avail. Birkir said it was unnecessary, but Hadrian was insistent upon finding a better name, thinking it would improve his lot in life. Eventually he asked to be called Henrik (after the ancient Nord, Sir Henrik, of the Knights of the Nine). When they moved to Riften, he told everyone that was his name. And it stuck.
Henrik was much happier in Riften until Birkir met and married Ysri Bjornsen and they had Trygve less than a year later. Henrik hated Ysri from the beginning and things only got worse when Trygve came along. As a full-blooded Nord, he was clearly destined to be the favored child. As they grew older, Trygve’s closeness to his mother was facilitated, in part, by his father’s need to keep Henrik under control. Ysri was incredibly compassionate but also fiercely protective and dedicated to those who came under her care and guidance. When he was younger, it was to his his mother’s standards as a healer and priestess that Trygve strove to live his life. She was, by far, his most significant influence and inspiration. She still continues to inspire him although it is unlikely that she would approve of some of the methods by which he accomplishes his tasks.
But Trygve was still close to his father who regularly took both boys hunting and fishing. Trygve was a natural archer, while Henrik struggled. Trygve grew tall and strong and was always highly disciplined and resourceful, while Henrik was strong, but stocky, and though he worked hard, he was always unfocused and lumbering. After a while, his only Nord talent was for drinking.
About a year after Ysri died, the tension with Henrik (who had been living at home and losing job after job due to his drinking) exploded and Birkir kicked him out. The tough love worked, however, and Henrik went to Castle Dour and joined the Legion where he became a decent soldier. Over time he was able to repair his relationship with his father and with Trygve, though they were never close.
After Henrik left, Birkir and Trygve enjoyed some peace and quiet though over the years Trygve began to grow restless. When he decided to travel extensively, Birkir was supportive but not pleased. He was hoping that Trygve would settle down with a wife and open some sort of business in Riften. He was devastated when he found out from Iona that their friend Jori died and Trygve had decided to stay in Solitude. They saw each other a couple of times after that and the visits were always fraught with tension as Trgyve was very closed off, first about what happened with Jori and second, because he was in a tumultuous relationship and wanted to shield his father from that part of his life.
Birkir was thrilled when Trygve returned to the Rift and with Henrik stationed in Helgen, he was happy to have both sons nearby. When Birkir was struck with a terrible illness, Trygve worked relentlessly to save him. In his last days, he simply asked one thing of his younger son, that he and Iona take over his final duty, that of protecting the fugitive-from-the-Thalmor, Nerussa.