As a preface, I'm not trying to insult the quality of GRRM's works. Nor am I suggesting that my "additions"/"improvements" are of superior quality to the original novels or if it would even be workable in the narrative. Instead, I'm just putting in what I think (heavy emphasis on "I think", as it is just my opinion) would be interesting to see in the world of ASOIAF.
Here are some of my personal "changes" I would make:
With the Dothraki, I wouldn't make them civilization destroyers, as they were in the novels' backstory. As I don't think relatively under equipped and fragmented nomads like the Dothraki would have the resources for that. In my "reimaging", they are just a loose collection of nomadic tribes/khalasars. They are still a dreaded terror for small villages and weaker pastoralists, a considerable threat to traveling merchants, and have been known to devastate armies sent against them with guerilla warfare. However, unlike the novels, the Dothraki won't be conquering/besieging major cities, as they don't have the weaponry, manpower, or the logistics for such operations. In other words, the Dothraki genocide of the Sarnori and the Century of Blood wouldn't have played out in my "version" as the way they happened in the official ASOIAF timeline.
Thus, the Essosi city states consider the Dothraki to minor yet scary nuisances. They mostly leave the Dothraki alone, unless a Dothraki Khalasar raids one of their outposts/villages. In such a case, they will sent a punitive expedition to punish the offending Khalasars, and then leave. If anything, the Essosi states consider the Dothraki to be somewhat valuable trading partners. I picture the Dothraki trading animal furs and slaves to the Essosi city states, in exchange for livestock and iron tools.
Dothraki subsistence also isn't dependent on pillaging. They extensively hunt and raise livestock (like sheep and goats) of their own. As mentioned in the previous paragraph, the Dothraki indulge in a lot of trading with other Essosi peoples. Last but not least, I would make the Dothraki much more akin to Great Plains Native Americans then to Turco-Mongols.
Like the Dothraki, I would dampen the Ironborn obsession with raiding coastal settlements (though they still extensively practice it), and get rid of the taboo against trading. As no society could function without a viable source of subsistence/income. In fact, they have extensive trading contacts throughout Essos and the Sothoryosi islands. The Ironborn also don't contain any noble houses in their political system, though other Westerosi erroneously view their chiefdoms as a noble house. Similarly to how the ruling Northmen viewed the Northern Mountain Clans as petty noble houses in the novels.
On that same note, Ironborn don't have a Monarchy in the classical sense of the term. They elect their kings, who are selected from the warrior elite. Relatives of Ironborn kings nominally don't have any power, but their brothers and sons have a strong possibility of succeeding him if he proves to be popular.
Their islands would be more remote and fortified against foreign enemies. The Iron Islands would also be much larger (perhaps around the size of Alaska) and mountainous. So the Ironborn will have a sanctuary to hide in, if a punitive force shows up to wipe them out.
As with the books, they are their own kingdom in all but name (to the point of having foreign policies independent of the other 7 kingdoms), and do everything in their power to undermine the Iron Throne's authority on them. They also despise how the other Westerosi try to enforce their morals on them and their attempts to criminalizing many Ironborn traditions and customs. Like their worship of the drowned god, slavery, and polygamy.
I would also put far more emphasis on the Basilisk Isles then in the actual novels (I think they were only referenced in four or five passing sentences in the books, and are almost totally ignored in supplementary materiel). In my "reimagining", the Basilisk Islanders would be a tribal confederation of piratical seafarers. Most of their numbers consist of natives, but they accept outsiders from all across the known world into their ranks from time to time. They often hijack merchant ships passing through the summer seas and raid other islands for slaves. Captives and loot seized in their raids will then be sold to slave markets in the Free Cities and Slaver's Bay.
If a merchant ship doesn't want to be boarded, the captain would have to pay for the chieftain's (or "corsair king" to outsiders) permission to sail his waters. Basilisk Islander Chiefdoms also form overly convoluted and two faced arrangements with the warring Free Cities. Often times, Free City states will commission Basilisk Islander tribes to disrupt the shipping lanes of a rival. These "alliances" tend to be tenuous at best, and break and form on the drop of a hat. When a client Basilisk Islander tribe falls out of line, a Free City will send an punitive expedition to stamp them out.
However, the Basilisk Islanders are far more then just over glorified pirates and privateers. Basilisk Islanders have been known to engage in peaceful trading with Essosi and Westerosi kingdoms and city states. They are also agriculturalists, and a primary food source for them is their own crops.
In addition to the indigenous tribes, there are a number of rouge settlers (mostly criminals and runaway sailors from all across the nine Free Cities, but especially from Lys, Myr, and Tyrosh) that make their home in the isles. As with the natives, the settlers frequently attack passing ships and indulge in slave raids. The relationship between the settlers and the native Basilisk Islanders varies considerably, depending on the circumstances and individuals involved. Sometimes they collaborate in piratical endeavors rather seamlessly, but bouts of violence between settlers and native tribes do occur from time to time. Unlike colonial era Euro-American settlers in our world, settlers from the Free Cities don't have the manpower, equipment, or support to uproot the endemic powers.
I will add more, if I can think of anything else.
If you could add or change anything in ASOIAF's world building, what would it be?