I don't know if this answer is consistent with subreddit standards, but I feel like I need to ask a clarifying question first. What exactly do you mean by trades here? Like the control of specific commodities? Or the regulation of trade? Or control via taxation rather than outright bans? The part I'm struggling with the most here is the point about the colony "dependent" on the colonizer. I can't speak to settler colonialism of the early modern era. But in the modern historical period, the "colony" was almost never dependent on the mother country. The opposite was true, and it was the colonizing country which needed the colony as a market for its industrial goods and a source of cheap raw material. That's why the clarification is important.

Because depending on how you clarify it, the answer could vary. For instance, in British India, there were a bunch of different policies. Some were aimed at protecting commercial interests of the metropole (Britain) over industries in India. Others were simply outgrowths of wanting to increase revenue.

There was for instance the Opium Trade in the 19th century. For the British in Asia, Opium was the commodity by which they acquired Tea in China, to the point that they even fought two wars to force the sale of Opium in China. In India this resulted in the very careful control of the commodity, so that Indian farmers were both actively encouraged (sometimes even forced) to grow Opium, and then found their ability to sell the crop heavily curtailed to ensure that British merchants could acquire it very cheaply, and then sell it for increased profits on sale and exchange for tea in China.

This similarly played out with the textile industry in India. Indian textile makers found their ability to sell heavily regulated so as to favor merchant interests, and in the long run ensure that Indian raw commodities for textiles acquired cheaply. Later, as the British textile industry grew during the first wave of British industrialization, it was about ensuring that English merchants didn't face any competitive threats in India, and could thus dump product in India cheaply for high profits. This lobbying by the textile interests in places such as Manchester would have a profound impact on British policy in India for decades (centuries even, insofar as it lasted over 150 years) as the British government was naturally much more responsive to mercantile interests in Britain than constituents in India to whom they were never answerable to.

You'll want to check out Prasannan Parthasarathi's The Transition to a Colonial Economy for a breakdown of the ways in which British policy was enacted to deliberately marginalize Indian textiles at the expense of British mercantile and textile interests. Some historians have argued that this constituted a form of deindustrialization in India, though its a somewhat controversial term. It also featured prominently in early 20th century Indian rhetoric on the "drain of wealth."

Another aspect of British policy was about controlling Indian fiscal policy and industrial access. Thus for instance after World War I, the British were eager to create a system of "Imperial preference" which, in simple terms, basically meant that there were zero tariffs in trade between colonies of the empire and massive tariffs in trade outside it. This naturally suited British industrial interests which were relatively advanced (and because Britain could independently create special access for important markets like the US) and screwed colonial industries who wanted a different level of protectionism and access. Industrialists in India for instance were demanding general protectionist policies, while also pushing to be allowed access to emerging Asian markets such as in Japan. The Imperial Preference policy was enormously controversial and spurred nationalism in India. And it was a policy aimed at keeping the colonies tied together, though not necessarily "dependent" on the mother country.

See Basudev Chaterji's The political economy of ’discriminating protection’ : the case of textiles in the 1920s. https://journals.sagepub.com/doi/10.1177/001946468302000301

Basically fiscal policy and the Imperial preference system was another way in which trade was controlled to favor the Empire. Some of it included outright bans, but not always.

Finally there were taxes. The most notable in South Asia is the salt tax. Indians were simultaneously prohibited (with criminal sanction) from making Salt, even if they literally lived right on the coast (and India had some pretty massive coasts) and were forced to buy Salt from government sources. This salt often had significant taxes on it. Salt, like grain, is an essential commodity. Gandhi would make this the focal point of his protest against Imperialism, alleging that the Salt Tax was inherently exploitative and aimed at sustaining imperial interests and controlling Indians. His Salt Satyagraha, where he undertook a several hundred kilometer march to the coast where he openly broke the salt law by making his own salt at the coast was a major turning point in Indian Nationalism.

As you can see, using just India, there's several different ways to approach this question. I'm hoping this has helped address the ways in which Empire could, through controlling trade, ensure its commercial, economic and strategic interests and thus sustain the Empire. But I remain uncertain about which aspect you're interested in insofar as "banning" and "trades" are concerned. Also, this question doesn't really address Settler Colonies like in the US. Imperial governments had other ways of controlling access there (famously Tea in the case of the US, by granting a monopoly to the EIC, and undercutting American smuggling which led to the famous Boston Tea Party). But Settler colonies aren't really my forte so I'm less certain about answering that. Also pure settler colonies represent a somewhat earlier phase of European imperialism, and one that was largely over by the 19th century. Australia is something of an exception here, but that's got its own complications what with it also working as a penal colony.