The default rules for demoralizing require a standard action and apply a 1-round shaken effect.
Intimidating Rage changes this to require a free action, and for the shaken effect to last as long as you rage.
Imperious Command changes the 1 round of shaken to 1 round of cowering followed by 1 round of shaken.
These two options replace some of the rules for demoralize; they are not applied as two separate effects. So the target will definitely not be frightened at any point; you will not be applying two separate shaken conditions. Unfortunately, that’s the last statement we can make with certainty.
How and whether you can apply two replacement effects to the same thing is not defined in the rules.
You could argue that they are both replacing the same thing, the rules for demoralizing, and cannot be used together at all.
You could argue that they are both replacing the same, but that thing is just the effect of demoralizing (and, in this argument, the fact that Intimidating Rage also replaces the action cost is a separate and thus irrelevant replacement). In this view, you could take advantage of Intimidating Rage’s lower action cost and combine that with Imperious Command’s effect, but you would still get only 1 round of cowering and 1 round of shaken.
You could argue that they don’t change the same thing, as Intimidating Rage is changing the duration of the shaken effect while Imperious Command is inserting a round of cowering first, so you get 1 round of cowering followed by them being shaken as long as you rage.
Any of these has validity, and might be true. There are not enough details to say. You’ll have to ask your DM. Ultimately, Intimidating Rage is replicating a lot of the default rules for demoralize in its own text, and it’s unclear how much of that is just a reminder of how everything it’s not changing work, or if those are reiterations of those rules to somehow “enforce” them in the face of other options (like Imperious Command).
On a complete side-note, if you’re interested in demoralizing, you should also look into Never Outnumbered from Complete Scoundrel. Though you would have even more confusion about how or whether it could combine with Intimidating Rage.