The way I see it, it looks like your Project Managers are having difficulty getting the work done out of their teams. The Project Managers should clearly draw lines around what the team-members are supposed to do as per their Job content and not make it look as if they(the team members) are doing a favor to them(PMs). Either this, or the PMs are mis-communicating with their team, committing to things that they can't really assure and the team is getting frustrated by it. I would suggest putting your Project Managers through a Leadership training with special emphasis on communication - especially with Power and tact. Before you meet prospective training providers, understand some special scenarios in the past to explain to the providers as ''pain points'', so that the trainers come up with relevant situational roleplays.
Hope this helps!