The Kingdom of Kolyma has several meanings, it refers to the entirety of the western side of the mountains (the Land of Kolyma, where Valanice is said to dwell), possibly to eastern Kolyma or the entirety of the continent of Kolyma.
Background[]
The Kingdom of Kolyma (eastern Kolyma) is largely difficult to reach, and most travelers apparently use the Magic Doors to travel there and back.
Due to the remoteness and dangers of the western side of Kolyma's continent, most good folk make their homes on the eastern side of Kolyma, separated by a spine of high mountains and a great chasm from the greater horrors. The royal family live in a castle there. Only a magic door grants passage from east to west, and even this will send someone elsewhere if they have not the proper key. A great strangeness folds the western land back upon itself to both the north and the south, forever bringing travelers back to where they started. All these barriers have, with only occasional exceptions, kept them isolated.
The parents of Valanice, Coignice and Cedric appear to be from eastern Kolyma, an area about which almost nothing is known. Some maps show it to be a very thin area of cliffs and beaches on the far side of the mountains (with Enchanted Isle of it’s coast), or thicker region with its own forests. It's also know that there is a castle there as well where Valanice grew up, and where most of the population lives.
The Blue Beach (Strange Beach) to the west of the Enchanted Island appears to be the eastern shoreline of Kingdom of Kolyma (eastern Kolyma) on one of Derek Karlavaegen’s maps, and he also has said the use of Magic Door with the correct key allows passage to eastern Kolyma. Which means the Enchanted Island also lies to the east of Kolyma, or south east as seen on the map.
Other theories, however suggest its yet another island of the Blue Islands/Enchanted Isles chain. The existence of this region is usually debated to be far away from the continent of Kolyma, on the other side of the world, or possibly even in another dimension.
The Kingdom of Kolyma can also refer to the entire known kingdom which is divided by the mountains into western Land of Kolyma and the eastern kingdom. With most of the population living in the smaller eastern region, and larger and remoter western region ("Land of Kolyma) having fewer inhabitants. The region includes the entire known continent: the Land of Kolyma (western Kolyma) and eastern side of the kingdom beyond the Forest Mountain, passed the Top of the Cliffs.
Although sometimes the Land of Kolyma (western Kolyma) is also referred to as the Kingdom of Kolyma by itself, though its actually only the larger portion of the kingdom as a whole (and some might argue makes up the main region of Kolyma).
Behind the scenes[]
The term kingdom of Kolyma or Kingdom of Kolyma appears on certain versions of the KQ2 box, and in the KQ2 manual in the prologue story: Romancing the Throne by Annette Childs, in KQ4 manual; This is the legend of King's Quest..., and in KQ7 Hintbook: A Summary of King's Quest. In which it is said to be the home of Valanice, and is the land Graham visits during the game. The use of Kingdom of Daventry appears in the game files itself, but doesn't appear to be accessible. So from the game's perspective Valanice's homeland is the Land of Kolyma ('western Kolyma') visited during the game. Though its never clear where she actually lived in that land. Though the Home Amulet takes her back to the Monastery strangely enough (though its also possible it brought her back elsewhere, and time passes before the scene in the monastery).
Most hint guide maps calls KQ2 kingdom, the Land of Kolyma (and box maps divide it into 2-4 parts making up East Kolyma and West Kolyma).
The King's Quest Companion adds the fact that there is an 'eastern Kolyma' beyond the mountain range where the main population for the kingdom lives, and was the original home of Valanice's family (but not specifically in relation to her, but rather where they currently lived). Though this concept is not really discussed anywhere else.
Some fans speculate that Castle Dracula used to be Valanice's and her family's castle. Although this is not ever confirmed, and is potentially denied in the King's Quest Companion (based on where it says her family's homeland is). The novels never mention the name of her country but does confirm she grew up in a [[castle (but never specifies where that castle was located) and that her homeland was home to 'fairies', and also discusses that Matilda her lady-in-waiting originated from there. Thus it can only be assumed that this castle was in 'eastern Kolyma', but also that when the novels talks about her homeland that it is referring to Kolyma in general (that all of Kolyma is Valanice's homeland). On the other hand it’s possible that the castle mentioned in the novels was a reference then well known castle from KQ2, or it was just coincidently invented by the author.