In trying to figure out how to do this, I found several unanswered posts related to this but it took me a while to figure out so I thought this might help somebody.
If you create a custom relate field (in my case prior_meeting_c in the Meetings Module), the field shows up as prior_meeting_c in an API retrieve as expected. However, to update the field you have to use meeting_id_c.
To get that name, I looked at the fields_meta_data table and looked for records with vname like ‘prior_meeting’ which showed two results: prior_meeting_c and meeting_id_c.