This is a great question–Unfortunately I can't speak to the chamber/bedroom side of it, but I can talk about the parlor/living room side of things some, at least in an American context.

I think it is important to understand that there is never a perfect correspondence between the names we use for spaces, the spaces themselves, and the way those spaces are used. So, the shift from talking about parlors to talking about living rooms might reflect the creation of a new type of room, it might reflect a change in the way rooms were used, or it might just be drift in language, with one term coming to replace another. The other thing to understand is that there is always a divide between the ways that architects, home magazines, and domestics "experts" intend for certain spaces to be used and the ways that they are actually used in practice. That said, let's get started:

One of the earliest styles of home in North America is the “hall-and-parlor” plan, where the first floor would be split into two rooms: hall and parlor (duh). A variant of this is the “center-passage” plan, where the hall and parlor were separated by an entry hallway, often with stairs leading to chambers above. In this system, the “hall” was a multi-purpose room combining cooking, cleaning, and often family dining and socializing. In theory, the parlor was a more formal space, used to entertain guests, or perhaps for family dining or socializing. In practice, this division was enforced more or less rigidly. In some cases, the parlor may have been a truly genteel space, in others it might be used as a bedroom, or a general-purpose room indistinguishable from the hall. This would depend on a variety of factors: ethnicity, class, size of house, size of family, etc.

In the 19th century, under a lot of different influences, many American homes became more complex, less symmetrically planned, and contain a wider variety of spaces. There was also an increasing interest in separating the informal and formal parts of the house. An example of the latter trend, if not the former, can be seen in the prototypical house plan promoted by Catherine Beecher in her book, The American Woman's Home. This plan is effectively a center-passage plan, with a few variations. One unlabeled room, is used for dining, sleeping, and family socializing, and is provided with movable screens that can create some degree of separation between these different functions. The other room, labelled "drawing room" but effectively a parlor, is used exclusively for genteel uses: "reserved for the reception-room of friends, and for our own dressed leisure hours," in Beecher's words. The kitchen is shrunk into a kind of "galley kitchen," connecting the two spaces and tucked behind the stair hall.

It may seem odd to promote the idea that half of the house should be dedicated to receiving guests, but this is in line with the so-called "cult of domesticity" that Beecher helped to promote during the 19th century. This "cult" held that the world was divided into the masculine, rough, exterior world of work, labor, and industry, and the feminine, refined, cultured, and restive world of the home. This ideology of "separate spheres" promoted the creation of formal, beautiful, and artistically decorated interior spaces that would soothe the nerves of weary husbands, and would inculcate good manners and Christian values in children.

(Of course, the problem with the "separate spheres" idea, is that the home continued to be a space of work. A side effect of this is that kitchens began to shrink, and be tucked away towards the back of the house as a kind of specialized workspace, with no space in them for socializing or dining.)

Beecher's exact plan was never very widely adopted, and home builders in the 19th century began to favor complex, asymmetrical plans with a variety of rooms, partly enabled by the adoption of new house-framing systems that enabled greater flexibility compared with earlier timber-framing. But the broader idea of creating genteel spaces within the home was widely adopted, and many many homes created in the 19th century had formal "parlors" that were, in practice, reserved for receiving guests, or interacting in a refined manner. These spaced would be "artistically" decorated, carpeted and curtained, and would include new mass-produced artistic experiences: print reproductions of paintings or biblical scenes, photographs of relatives or famous men, perhaps a family bible, as well as factory-made furniture featuring patterned upholstery and carved detail work. These sorts of spaces became a near-ubiquitous part of middle, or upper-middle class American homes in the 19th century.

This model came under attack however, towards the end of the 19th-century. Increasingly, these sorts of spaces were seen as being characterized by an excessive, even stifling formality. Female domestic writers began to argue that these spaces were difficult to clean, and that all the drapery provided space for dust, or unclean air. Male writers argued that parlors were too feminine, overly aestheticized, and impossible to relax in. The Ladies' Home Journal, perhaps the most widely-read magazine in America, began a dedicated assault on the parlor in the late 1890s, refusing to publish house plans with parlors in them.

Into the void comes the living room. This was driven by a few different cultural shifts. Domesticity in the late 19th and early 20th century was increasingly interested in efficiency and cleanliness. Parlors were associated with certain trends in decoration, including lots of drapery, carved wood, carpets, and little nooks and crannies that could collect dust. As a result, domestic reformers advocated for spaces that were more simply decorated and easier to clean. The domestic ideal also began to emphasize relaxation over sophistication, and embraced a kind of neo-rustic simplicity over the Victorian ideal that emphasized beauty as a means of cultivating taste and Christian values.

There is bit of a paradox here. Homes at the turn of the twentieth century were on the one hand striving towards a kind of rusticity, looking backwards from the overly formal Victorian fashions. On the other hand, homes were looking forwards towards new technology, and new ideals of sanitation and industrial efficiency. As a result, these new plans almost never combined “living rooms” with kitchens, as had been the case with the 18th century “halls” in hall-and-parlor houses. The kitchen remained a dedicated workspace, separated from the rest of the house. It would not be until the 1920s or 30s that “open kitchens” were more widely adopted, with a real pickup after WWII.

In any case, the parlor did not fit in with either ideal: it was neither rustic and informal, nor modern and “efficient.” As a result, it was increasingly rejected by architects and domestic writers. Again, there is a bit of ambiguity. In some cases, living rooms were formally different from earlier parlor plans: they might be open to the dining room, or maybe even to the stair hall. In other cases, the "ban" on parlors in the Ladies' Home Journal plans really was just a question of labelling the room differently, with the change in language reflecting a different kind of use, but not a different architectural form. Given that many Americans did not actually use their parlors in such a rigidly formal way, the rise of the living room may have been a purely linguistic shift for some, with no attendant change in either architectural form, or use. Also, it is worth noting that many people may have continued to like parlors and the attendant ideals they carried with them, even when architects and domestic reformers told them they weren’t “supposed” to.

Hope this helps! Happy to recommend more reading.