You have touched upon THE most important theme in The Home and the World: nationalism! This is so because the entire book is a reaction to the Swadeshi Movement which is precisely the drive towards Indian independence from British rule and, therefore, nationalism for that particular cultural group. Nationalism, of course, is the idea that every ethnicity (or ethnic group of people) should be self-ruled, and not governed over by any other ethnicity or authority. It is this detail, the specific name of the movement (the Swadeshi Movement) that is the most important detail in regard to the concept of nationalism in The Home and the World.
The first (and very important) detail to reveal is that Tagore's book is actually about the "second" Swadeshi movement, which is about the partition of Bengal. This partitioning by Britain was meant to weaken Indian nationalism in 1905, and the result was this Swadeshi movement which was specifically a boycott against all things imported from Britain. (Even pieces of clothing from the West were burned in large bonfires.) Gandhi had Swadeshi as one of his key strategies of self-rule in India, although he remained loyal to the Crown.
What is extremely pertinent, however, is Tagore's personal thoughts about the Swadeshi Movement and nationalism itself. Tagore was one of the original founders of the movement, but he turned against it when large scale violence broke out against Hindus and Muslims. The Home and the World is Tagore's full explanation (in numerous, personal accounts) of his reasoning for leaving the movement.
In context, this nationalism takes place in the story of Bimala. Why is the woman the main character here? The answer can be found within the text itself:
Men can only think. Women have a way of understanding without thinking. Woman was created out of God's own fancy. Man, He had to hammer into shape.
Bimala, noted as being the "Queen Bee" of the Swadeshi movement, is married to Nikhil, but falls for the idealism of Sandip, a Swadeshi agitator who has overstayed his welcome as a guest. Bimala even goes so far as to give Sandip money and jewels for the cause. It is the violence against the home, that of the Muslims who are planning an attack in order to kill Sandip, that makes Nikhil evict Sandip. Hence the title The Home and the World.
The first time Sandip comes to dinner, he urges her to remain with the men and take part in the discussion. Nikhil feels that he must invite Sandip to be his guest while he is in the area, but a few days stretch into weeks, and Sandip is still present. Although he admits to the reader that he believes strong men have the right to take whatever they want, he conceals his ruthlessness from Bimala. Instead, he flatters her, calling her the “mother” of the Swadeshi movement, or the “Queen Bee.” Though Nikhil’s old master, who is visiting, urges him to get rid of Sandip, Nikhil knows that Bimala would not permit him to evict the agitator. However, when he learns that the Muslims are planning to attack his home in order to kill Sandip, Nikhil informs his guest that he must leave. In the fray that follows, Nikhil is fatally wounded and Bimala has nothing to do but weep over her own foolhardy decisions. Note that it is the attack on the HOME that causes Nikhil to make his agitator "guest" leave. As one of our most prominent eNotes educators says:
The mere title helps to illuminate this. "The world" can be seen as the realm of social movements and political ascendancy, while "the home" can be seen as the subjective psyche that underscores all else.
Therefore, we can see that there are actually two types of nationalism here: the home and the world. They are very different. Further, they are exemplified by the two main characters: Sandip and Nikhil. As a result, this becomes Tagore's darkest novel of all. In the end, it is the violence of conflict that is the main evil here.
You are dark, even as the flints are. You must come to violent conflicts and make a noise in order to produce your sparks. But their disconnected flashes merely assist your pride, and not your clear vision.
Therefore, nationalism, even within the Swadeshi movement in India, isn't as important as a peaceful existence within the home and within the world.