I've been letting the original question rattle around in my head, and I can't quite decide exactly what my answer is.
I think it depends on how Ennis and Mr. Twist relate to one another: as ranch hand and employer, or as Jack's lover and Jack's father?
As Mikaela, Katherine, and Penthesilea have said, Ennis tends to be pretty deferential except in the circumstances that lead to fights. And I would add that, as an employee, Ennis seems to be very responsible. ("We're supposed to guard the sheep, not eat them." "We've got to stick this out, Jack." That look of guilt when the sheep is dead after the first night in the tent -- and I know there's a lot more symbolism in that scene than that, but I think Ennis-the-responsible-worker is part of the dynamic in that scene. And then later on, all those times when Ennis skips out on Christmas to do ranch work, or drops off the girls with Alma because the heifers are calving, or goes on a round-up instead of taking his one-weekend-a-month with his daughters.) And Ennis also doesn't tend to rebel -- he seems willing to take orders that aren't reasonable (sleep-with-the-sheep-no-fire), or to work long hours without getting much in return.
The exceptions, the times Ennis does rebel or complain, all are tied to Jack. Jack's the reason Ennis orders soup, even though it's hard to pack. Jack's the reason Ennis poaches an elk (and yeah, that's a compromise, but it's still against the rules). Ennis switches assigned jobs after Jack complains. Ennis stays in camp longer than he should, and eventually spends the night there, because he likes being with Jack. Ennis complains about Aguirre cutting them out of a month's pay because Ennis doesn't want to leave Jack. And later on, Ennis quits jobs so he can go on the "fishing trips."
Ennis's violent streak, as Mikaela pointed out, always seems tied to comments about Ennis's sexuality. (I might go so far as to say that Ennis gets into fights because of the conflicts going on inside him, almost as if Ennis is trying to beat his sexuality into submission by hitting other people.) So a lot would hinge on how much Ennis had come to accept himself in order to try to live the "sweet life."
And as for Ennis's relationship with Jack's father -- well, I think that would depend a lot on how Jack dealt with it. If Jack's father avoided Ennis, and Ennis just did the work and avoided Jack's father, then they would probably be able to co-exist. But if Jack's father treated Ennis badly -- I could see Ennis just taking it, as long as Jack's father didn't manage to hit one of Ennis's sore points (and then, watch out -- Ennis is like a dormant volcano, I swear). But Jack complains when things don't seem right to him. (Bitching about Aguirre's orders, complaining to the teacher about his son, backing up Lureen at Thanksgiving. And, of course, "no more beans.") And if Jack complains, Ennis does something. Not exactly what Jack wants, not most of the time. But Ennis does something. (And if Jack and Ennis moved up to Lightning Flat, that would mean that Ennis became more likely to give in when Jack wanted something, not less likely as in the movie/story.)
Katherine: I interpret "though he was too special..." as referring to a lot of different things -- maybe partly to Jack's sexuality, but also to the fact that Jack left home, moved to Texas, and never even brought his wife and baby to visit them. Yes, they could have gone to Texas to visit as well, but Jack's father just seems so typical of all the old rural families that I have known who watched their kids move away -- even the really nice parents get resentful of all that separation from their kids and grandkids.
Jeff -- yes, I think that the Twist ranch would have been the most economically viable option for Jack and Ennis. It's strange that movie-Jack mentions things like Ennis moving to Texas late in their relationship, but never mentions Lightning Flat as an option. I know that Ennis is really twitchy about the whole living-together thing, but from a practical standpoint, the Lightning Flat option has a lot going for it. It just might work financially. It's at least in Wyoming, even if it's pretty far from Riverton, so it might be practical for Ennis to see his daughters once a month. And if Ennis was really afraid of living openly with Jack, they could concoct a reasonable cover story about being a ranch owner and foreman. (In an ideal world, they wouldn't need to, but Wyoming is hardly an ideal world.)