I don't know which novel you're referring to because you didn't provide enough information. But generally speaking, the plot of the novel was fictional, so the situation of the child born by the demon king and the nanny also depended on the plot of the novel. If you can provide more information, I will try my best to provide you with a more accurate answer.
If Tanjiro becomes a demon in fanfiction, he might lose his sense of humanity. His relationships with his friends and family would be severely strained. For example, his sister Nezuko, who is also a demon, might be affected in unexpected ways. He could struggle with his newfound bloodlust and the need to consume humans, which goes against his original kind - hearted nature.
Tanjiro and Kanao's love is a slow - burning and sweet one. They first meet as comrades in the fight against demons. Tanjiro's kind heart and strong will gradually draw Kanao out of her shell. Kanao, who was initially rather reserved, starts to open up more because of Tanjiro. Their relationship develops as they face numerous challenges together, and their mutual respect and growing affection for each other are heartwarming to watch in the series.