It looks as if the people that founded the Corded Ware culture, largely eliminating the previous LBK-like farmers, were the Yamnaya, themselves a mixed population, approximately half some kind of eastern hunter-gatherer and half some farming populations genetically similar to Armenians.
In which of those two populations did primitive Indo-European – the language – originate? I’m betting on the hunters. I suspect that they’re the ones that domesticated the horse: horses weren’t very common south of the Caucasus, and it doesn’t look as if they were domesticated there.
It’s not easy for farmers to conquer horsemen: easy the other way around.
The dominant Y-chromosome lineages among the Yamnaya (and later, most of Europe and India) originated in those hunters, not in a Middle Eastern population. It is hard to believe in a scenario in which the farmers conquered the hunters and then forced their women on them (Take my wife, please!).
Analyzing old myths and legends, various people smoking superior kinds of dope have argued that there was a ‘war of the functions” – formation wars – at the beginning of the Indo-Europeans, where a group of warriors and priest/magicians/judges conquered farmers. Two estates absorbed the third. Possibly referenced in those sobbin’ women, the Aesir-Vanir war, the Mahabharata, etc.
Moreover, something relevant happened earlier, before the Yamnaya made their big move. Somebody – pastoralists – smashed Old Europe in the Balkans a good deal earlier, and someone (maybe the same people) brought a very early branch of Indo-European into Anatolia ( Hittite, Luwian, Palaic, Carian, etc. ) Then there are the Indo-Aryan languages, and Tocharian: looking at those branches, and the genetics of early speakers, should resolve this problem. For example, if you find a population of Indo-European speakers that has that eastern hunter-gatherer genetic signature, without the Armenian-like signature, probably the language originated in the hunters. Or vice versa.