How to tell my PhD supervisors I want to publish without them? 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.
Based on your account, I am surmising that you have already completed your PhD thesis, and obtained an academic position independent of your former supervisors (well done!). That being the case, you are under no obligation (whether legal, pragmatic, or ethical) whatsoever to involve your former supervisors in publication plans for work to which they did not make an author-level contribution. If you feel that (and, now that you are a Doctor of Philosophy, you should have some confidence in your academic judgement) you will advance scholarship more effectively by publishing alone or with different collaborators, you should have no qualms about doing so.

By the way, in my humanities field (in which sole-authored publications are the norm), it is perfectly acceptable, even encouraged, to publish without your PhD supervisor while still a student. I have two excellent supervisors, but it has never occurred to any of us to pursue a joint publication. In fact, funnily enough, I have recently completed a sole-authored book-chapter for a collected volume in which my principal supervisor just happens to also be writing his own sole-authored book-chapter (on a different topic, although relevant enough that I actually cite a few ideas from his chapter in mine).