Two things here:
The Hydra agents were all "sleeper" agents. As such, they'd have been ordered to act as loyal, effective S.H.I.E.L.D. agents right up until the moment that the higher-ups "activated" them to take over the agency.
I suspect that getting Hulk onto the Avengers over Abomination may actually have been intentional on Pierce's part, given what he, and most other people, knew about the two "monsters" at the time.
I think you can get a better picture of what was going on at S.H.I.E.L.D. vis-a-vis Hydra from the TV Show, since that spent a lot of time with the rank and file agents. Since they are set in the same continuity, anything we learn on TV must apply equally to the films.
There, we see quite a few undercover operatives on the TV show going out of their way, even risking their lives, to try to stop activities that were ultimately being conducted by Hydra itself, because that's what a real agent would have done. We can only assume that the Hydra top brass were being kept appraised of their agents work, including anything the agents were being asked to do that went against Hydra plans. Had they forced those agents to intentionally tank their own missions, at best those agents would have been taken out of the field, and at worst, exposed as traitors. Instead, the Hydra leadership simply allowed S.H.I.E.L.D. to thwart their plans when needed, and adapter in response. If Sitwell felt that his undercover persona would have worked to undermine Pierce's orders, he would need to act that way to remain undercover.
In this case, however, I'm not sure that Coulson and Sitwell's plan was even counter to Hydra's goal. From what we can tell, a big part of their plan was to discredit S.H.I.E.L.D. as an agency, and destroy its ability to act, so they would be able to operate freely in the aftermath. Considering what we know of the two gamma-induced monsters, which of these sounds more reasonable to an outsider:
- A trained, highly decorated special forces soldier, who was the subject of a controlled experiment by the US Army, who is in complete control of his mental facilities, or
- A mild-mannered scientist who was subject to a radiation accident, that has no control over his transformation into the Hulk and loses almost all of his cognitive abilities when he does so, that spent years running and hiding from the military and, in certain people's views, stole crucial military secrets in the process.
Remember, the plan was to blame all of the carnage from Blonsky's rampage on Banner, making Hulk look like a rampaging monster and Blonsky like the hero that came in to save him. We, and a select few like Coulson, knew full well that Hulk was a better choice for the Avengers, but from an outside perspective, Blonsky seemed to be the hands-down favorite.
I suspect that Pierce knew full well what Sitwell was planning to do. At his level, he could easily have intervened after the fact to fix Coulson's sabotage, but he didn't. He likely expected that hiring Banner would backfire spectacularly on them, and when Hulk went on another rampage, it would make S.H.I.E.L.D. look bad. When it came out that they could have had Blonsky on the team, but two lower-level agents purposely sabotaged that plan, it would only further the idea that S.H.I.E.L.D. was corrupt from the bottom-up. Both of those things, ultimately, play into Hydra's plan just fine.