OOC: Sounds like it's time for a map update. Care to share the size and location of Boer and Lakota?
The Great Veldt is pretty much the US great plains, so figure the Lakota to be in OTL Minnesota, the Dakotas, Iowa and parts of eastern Montana and northern Nebraska with a chunk of northeast Wyoming. The Boers (having a large mestee population, and most importantly, guns and horses) have carved out a rather large territory stretching from OTL middle to western Montana in the north down through middle to western Wyoming, Colorado, southern Nebraska, Kansas, Oklahoma and Texas (north of the rio Grande, with a big chunk of New Mexico east of the Rio Grande, and have even reached the Great Salt Lake. They accquired the vast quantity of land through a combination of armed conflict and intermarriage with the "abros" of The Great Veldt and (perhaps) a bloody war with Mexica over "The Texas" as the Boers called it.
[The Boers, in TTL, I see as a sort of fusion of OTL Boers, the Scots Irish settlers of the mid-Atlantic and sourthern British colonies (OTL) and French Canadian voyageurs (OTL), culturally.]
The Boers origins (ITTL), The Great Trek (ITTL and the reasons for it) and the Boer settlement of The Great Veldt would make for a couple of epics in themselves, actually.
Already have the basis for the first two formulated, actually, and have it in mind to write them out. Perhaps another thread, fleshing out the established cultures in this world would be something to explore this interesting little world a bit further.
One thing about Nieuw Nederland: the Dutch (IOTL) actually established claims to the whole of OTL Connecticut and Rhode Island. Without the English Mass. Bay colony, I could see them settling as far north as The Grote Baii ITTL (due in large part to TTL's Boers). Perhaps OTL New Hampshire ends up a buffer zone between NN and Vinland ITTL, perhaps not. Makes for an interesting disputed area too. Also OTL Pennsylvania would (again due in large part to TTL's Boers) be part of Nieuw Nederland as well. (Partially due to OTL Dutch claims and, yet again, to The Boers settlement of these area...which I assure you, they had very good reason to do.)