In the short term, there was hardly any immigration from Europe to Greenland. Almost all settlers of Greenland came from Iceland, not Norway or Scotland.I don't think a significantly larger "seed" for Vinland is plausible, so I'll focus on them working things out with the Skraelings.
In the short term, there would be some immigration from Europe to Vinland.
Where?The Norse would inevitably launch further expeditions, and would soon find that there were better lands to the south. But even with the attraction of new lands, the sheer distance would limit the flow. It wouldn't take long for locally-born Vinlanders to outnumber immigrants.
I agree that the idea of Vinland being anything but a nominal subject of a European king is implausible. The question is, what would the local government look like? I think the original Vinland colony would probably follow the Icelandic model, but I imagine that some adventurers might found kingdoms of their own elsewhere.
There are certain things with Icelandic model:
1) Iceland was uninhabited all around. The first settlers of Iceland, 435 of them, were free to settle anywhere around the empty coast.
Newfoundland is almost exactly as big as Iceland - slightly bigger - but possesses the Skraeling populations. Settling in an outport involves dealing with neighbouring Skraelings... for which the newcomers from Iceland and Greenland do not have experience.
Therefore there is a strong incentive for the new settlers to NOT found new outports with no experience - a safer move would be to join an existing Norse settlement and rely on the old settlers for protection against Skraelings, interpreters and intermediates for trade etc. It would be years later, when they have got the feel of the geography and Skraeling language and acquired Skraeling friends and trade partners at the proposed new outport that they would be safe to move there.
And the dependent relationships from living for years in the settlement of an existing chieftain would tend to last - if the peace and trade agreements with Skraelings are made under an existing chieftain then settling new lands under protection of these existing agreements would tend to carry over a dependence from the chieftain whose agreements they were.
2) Icelanders had few ships of their own. Much of the trade was carried out by ships that sailed from Norway, and then around Iceland.
Since the settlers were scattered all around the coast, most of them could trade directly with a ship that sailed around Iceland. There was little reason for any place to be intermediary for trade. There was one region of Iceland that DID, however, have concentrated trade: on the southwestern plains, there was a large inland population, and sandy coast poor for landing which directed trade to a more suitable spot at Eyrarbakki. It is no coincidence that this region did already in early 11th century power the rise of Haukadalur clan, and then See of Skalholt.
So: Icelandic model was changing in 11th century, too. Vinland could evolve away from 10th century Iceland model for similar reasons... plus additional ones, causing the development to be faster, earlier and further.
Sami used iron, but did not adopt all Norse technology.And the Skraelings would quickly hit the Iron Age, so the Norse would lose their tech advantage.
Trade with Vinland would support Greenland better than the OTL trade with Norway did.The Little Ice Age would probably kill the Greenland colony sooner - the Greenlanders would probably choose to move to Vinland. There might still be a fishing outpost or two, possibly dominated by the Inuit rather than the Norse. This would probably cut off regular contact between Europe and Vinland, although there would still be the occasional ship making the crossing. Any nominal fealty would end.