Am I in the right

As you are approaching your customer say 500 miles out send a message that after delivery you need 12 hours off or whatever appropriate rest time you as a team want to take off.

 

Best example is the situation you described in Denver.

Even when you're on time for your delivery in Denver, you are already a minimum of three hours late for your pickup.
And those three hours is the time needed to make the trip more convenient and the job bearable for you.

If I'm getting dispatched too late I'm not sacrificing my time. I do what I can do but will also point back to them if they ask.

 

Some companies and dispatchers try to create the fake expedite culture to keep you running like a slave but if they are always taking last minute freight and making commitments like that the ball was dropped before you ever got the load and they are setting themselves up for failure.

Thanks to the driver making reference to fake expedite loads you put a name to a problem I suffered a lot from as a new driver. I always felt like I had to push it to the limit till I had enough close calls and made enough bad decisions to learn that my own well being had to be the absolute priority. Don't ever let them convince you some other company won't do a better job planning loads and be more accommodating to your needs.