All that plus, the Dothraki are a "kill the head the body will die" force
That's a pretty massive assumption to make given the little information we have. Oh, so after Khal Drogo's death the Dothraki army factioned off because they didn't want to follow a foreign Khaleesi? Gee, what a shocker! They were in their homeland. You think they'd react in the same way if they were in the middle of a war in Westeros (on the opposite side of the ocean)? And in a war where they'd seen their brothers, cousins, uncles, fathers, et al. lose their lives they'd just fall to pieces? I just don't see that. The battlefield has a way of unifying troops that is difficult to quantify. At the point of Drogo's death they were, at least in regards to that engagement, unbloodied. Were they to have actually invaded that would have changed quickly.