Stephen Covey's book, The Seven Habits of Effective People (1992), offers a conceptualization of how successful individuals handle concerns by managing those that they can do something about. Known as the Circle of Concern/Circle of Influence (pdf), Covey's approach works well to help co-teachers separate out issues given high priority for collaborating within a single instructional space.
By focusing on concerns that we can do something about, we can proactively expand our Circle of Influence. Conversely, if we attend to concerns over which we have little control, we place ourselves into a reactive mode that shrinks our influence. Communication is the key to effective co-teaching within a Circle of Influence! The more focused communication is on the Circle of Influence, the less time and effort need to be spent on resolving conflicting issues.
Here's an example of the two approaches in a co-teaching planning session:
Can you see how the 'Influence Question' would be more effective for co-teaching?
Put another way, think about what expectations you have for the shared instruction and what assumptions you make about the classroom and instruction. While these may not be concerns in the strictest sense of the word, they are essential to communication about how co-teaching will be implemented. To expand your influence, i.e., effectiveness in a co-teaching situation, you need to address these concerns with your co-teaching partner and come to a mutual understanding regarding the classroom environment, your individual and collective roles, classroom management, assessment/grading, and feedback, etc.