This depends on how far back you want to take things. In the medieval period, England generally claimed overlordship of Scotland whether or not they actually held practical power over it. There are many occasions in the chronicles when the Scottish king pays homage to the English king, or a treaty is established granting the English certain rights in Scotland, or the English invade Scotland because Scotland tried to raid the border and was put down hard. There were English nobles who held a lot of land in Scotland and Scottish nobles who held land in England. The relationship was complicated and often contested. In the dubiously historical Geoffrey of Monmouth, for example, the mythical hero Brutus comes to Albion (Britain) and pushes the native inhabitants (what would become the Scots) up into the northern part of the island, where he is content to let them stay. But in the same story they also fight giants, so I wouldn't lean on the story. However, the trend remains constant where England and Scotland push the other's borders, but England usually ended up on top.

Here are some places to start investigating further for the medieval period:

Cynthia Neville. Violence, Custom, and Law: The Anlgo-Scottish Border lands in the Later Middle Ages (1998).

Mark Bruce and Katherine Terrell. The Anglo-Scottish border and the shaping of identity, 1300-1600 (2012).

Andy King & David Simpkin. England and Scotland at War, c.1296-c.1513 (2012).

Ruth Blakely. The Brus family in England and Scotland, 1100-1295 (2005).

Hope this helps a litte.

Scotland "joined" England, Wales and Ireland through the Stuart dynasty's succession of Tudors. Stuarts were the King of the Scots and Elizabeth I was held the Crown of England and Ireland. Keep in mind however, Scotland and England/Ireland were separate Kingdoms and ruled separately by respective parliament. Its important to mention that Scotland was a land unto its own, and were very much "independent" from England during this time.

in 1707, the two crown would join through the Union of Crowns(I've been corrected and this is actually Act of Union), creating what is today known as United Kingdom. I believe both nations sent representatives to figure out the nuts and bolts on the Union of Crowns so it was very much agreed by both Scotland and England.