I kind of job share. I do one third, colleague does 2/3, we overlap for about 6 hours a week.
We are a good team, as in our skills don't really overlap so our strengths are quite distinct. The fly in the ointment is that she can be moody (So I never know which version of her I will get) and frequently takes the leader role (especially when under pressure) and dictates to me.
This issue has been tackled several times: first when I sat down with her to discuss it, then I raised the issue with our manager and most recently our manager tackled her as she noticed this behaviour herself. Each time colleague has been a dream for a month or so but reverts back to habit.
Behaviour is: withholding information (we are supposed to be able to step into each other's shoes on projects and so have implemented an info sharing system, which works to a point, but there is onus on both of us to fill in verbally at crossover), talking down to me, correcting my work unnecessarily, nit picking and changing/over-riding decisions I have made. Small paper cut things mostly.
The thing is I now dread going into a job I love. I feel that having tackled this issue 3 times and we are still falling into the rut again I need to learn how to be thicker skinned and to not be so bothered by her tetchiness.