I don't think they were bad fathers. I think especially Ennis was a loving father who really doted on his daughters. No, he wasn't perfect, but I think it's important to take in account the given time and place.
I think given the time and place, Ennis was pretty much involved in the upbringing of his girls (at least until the divorce). When they were small, we see him taking care of them directly when coming home from work (someone else has already mentioned this). He did either bring them to bed or has checked on them before we see him having sex with Alma - and he is shown to do these things naturally; Alma doesn't send him to see after the girls in the first scene. He did
not come home and relax and expect Alma to do everything else.
Sure he dumps the girls with Alma at the grocery store when his boss called - but he
was willing to take care of them when Alma was working and he wasn't. How many fathers of that time were willing to do so? Heck, how many fathers
today are willing to do so?
And what else could he have done in this situation? He could have organized someone else to look after the kids (Alma's sister for example). But he did say he was in a big hurry, so maybe his boss was very impatient and bossy, we simply don't know. And although Alma had a job, I don't think she was the main bread winner.
I think it's not a prove of being a bad parent when the parent who was destined to look after the kids on a specific time and date suddenly has something coming up which makes a change of plans necessary. It has happened in our family life more than once, on both sides.
And it's also pretty usual for parents to argue over it at such occasions or even throw a fit (as Ennis does with Alma's extra shift later in the movie).
Speaking of that specific argument:
From Amanda:
Still, I'm confused about exactly what Ennis is so angry about. Why is he freaking out about Alma working at this particular juncture? Alma's always worked. I mean, why is he blowing up about it now?
I don't think it was about her extra shift. I think it was just an example of the increasing tension and the toll the situation took on all persons involved. Perhaps the argument has begun over something completely different, or one or both of them was simply ill-humored and stressed out on this day.
The arguments Ennis brings are not at all strong, especially in the light that normally he didn't have qualms with Alma working and him seeing after the kids for that time. To me it seems he simply doesn't know what else to say and betakes to stereotypes just for the sake to make a point. Not an uncommon strategy in arguments. People often say things of which they know they're BS, just for the sake to make a point, or to further provokate the other one.
And Alma is not impressed by his behaviour at all, she knows how weak his arguments are. She yells back at him just as good. And also in front of the girls. Which is not the best thing to do of both Ennis and Alma, but does not necessarily result in permanent damage on their kids.