I have had poor supervision from both my supervisors, but one in particular. Overall, neither provided me much intellectual support while I was doing my thesis in psychology. Early on, they were a little helpful when I was recruiting for participants - they attended my ethics panel meeting and made edits to my ethics application. I hardly ever saw them or met with them to discuss ideas (like once a year). The analysis of my thesis was a sole endeavour. I received minor feedback with respect to paragraph structuring, spelling errors and grammar in the write up of my thesis. No substantial feedback that helped me with my analysis, theoretical arguments or conclusions.
Additionally, I have felt unsupported from a morale point of point. My main supervisor's communication towards me has been disrespectful and belittling. For example, she has embarrassed me in front of colleagues by implying that I overestimate my capacities on more than one occasion. Now that I have finished my thesis and have passed examination, both my supervisors are keen for me to publish and have asked to catch up to discuss manuscripts.
I'm at two minds now. I don't want to give them intellectual credit for the work I did on my own. Yet, I also don't want to break down the decent relationship I have with my secondary supervisor. I have relied on this secondary supervisor to provide me with a good reference that ultimately won me prestigious position at a university. So I feel a sense of obligation towards her. The two supervisors work closely together so I couldn't possibly imagine having one included as a co-author and not the other - it would be extremely awkward and not really accepted.
The other thing that's playing on my mind is my inexperience with publishing. I haven't published a paper in years and feel trepidation about venturing out on my own. The reports I received from examiners were very positive and both said that my thesis was well written and publishable. But I still feel unsure about how to proceed and would benefit from practical guidance.
Any advice on how I should proceed would be greatly appreciated.
Edit: To clarify, the supervisors have requested we work together on translating thesis chapters into publications. Not new research.