You negotiate the deal you want. The market will tell you if what you want is unreasonable based on your dispute, the merits and risks involved, etc...
You are right in that it is normally one or the other, not both. Your best bet is to discuss your concerns with the attorney and see if the two of you can come to a mutually beneficial agreement.
This answer is for general purposes only and does not establish an attorney-client relationship. Consult with an attorney if you need further assistance.
All attorney fees are negotiable. If the attorney you are interviewing does not want to his or her hourly rate, continue interviewing.
A proper response would require a thorough investigation into the history and background of this relationship. The information provided above is just that, information, to be used as you see fit.