From my experience as a psychotherapist, rather than run off the deep end trying to use hypnosis, I always recommend that to better remember dreams you must write them down as soon as you wake up, immediately, don't wait because once your everyday waking mind's memories, anticipations, dialogues start up it is impossible to remember one's dreams, except snatches of rare incredibly powerful or vivid dreams. The key is to keep pen and paper and light at your bedside table. Further, if one immediately on waking writes down their memory of their dreams, as soon as this writing is done, typically more memories will arise. Also as one rests to fall back asleep, another dream memory may arise and should be written down. One might label this process hynogogic, but the name is unimportant.   

I don't know about the research in general, but a fascinating early study that involved a variety of hypnotic states in a dissociated study is the following: Prince, M. (1910). The mechanism and interpretation of dreams. The Journal of Abnormal Psychology, 5(4), 139-195.

http://dx.doi.org/10.1037/h0070883

Abstract

Discusses dreams as a method of psycho-analysis. It has been observed that in dream analysis, data obtained in the hypnotic state were precise and vivid, unlike those obtained in the waking state. However, not all Ss can be hypnotized and there is a possibility of fabrication of dream material. The contents of dreams were often associated with thoughts in the pre-sleeping state, particularly the disconnected ideas which are passive in nature. Mental experiences and recurring dominant ideas also account for these contents. Understanding the motive and meaning of the whole dream is important in dream analysis, since they may express an important idea in a symbolic form. The mechanism of the dream process is explained by the principle of conservation of mental experiences. Some dreams persist even after waking, but they are subconscious. This is identified as the underlying feature of hysterical stigmata. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

Some other dream material with the same patient: Waterman, G. A. (1910). Dreams as a cause of symptoms. The Journal of Abnormal Psychology, 5(4), 196-210.

http://dx.doi.org/10.1037/h0073013

Abstract

Discusses the mechanism and interpretation of dreams. Dreams are examined as the causal factors of symptoms. They may be the source of depression in some individuals and these symptoms may persist. The manifest content of dreams is a distortion of a repressed wish of the dreamer. M. Prince (see Journal of Abnormal Psychology, Vol 5, 139-195, PA: 52638) has referred to this as the motive of the dream. Some cases are presented which show that following an emotional disturbance in dreams, the Ss experienced physical discomfort, depression, nausea, and headaches. Further, the symptoms were associated with the content of the dreams and were a conversion of the experienced emotional disturbance. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

See also Recent bibliography of sleep, dreams and hypnosis. (2002). Sleep and Hypnosis, 4(4), a7-a18.

Abstract

Provides a recent bibliography of sleep, dreams, and hypnosis-related literature, with a focus on sleep and sleep disorders. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

Dorcus, R. M., & Shaffer, G. W. (1950). Sleep, dreams and hypnosis. In R. M. Dorcus & G. W. Shaffer, Textbook of abnormal psychology (pp. 287-336).

http://dx.doi.org/10.1037/13236-009

Abstract

This chapter discusses the relationship between abnormal behavior and sleep, dreams & hypnosis. Theories and abnormalities of sleep are presented, as well as criteria used to prove the validity of the claim that hypnotic regression belongs in the realm of abnormal psychology. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

Very excellent answer from Dr Harrod.  This is a great method for dream remembering and analysis.  

Nonetheless it does not answer your question, which is a very interesting one. I have found in most subjects that almost any event in their life is recorded, and can be brought back under hypnosis.  Certainly any event they thought was important can be brought back.  But I have never tried to have a client recall a dream while under hypnosis.  Good question!  Will be watching for answers.

 Thank you to you all for these answers. I'll try to make the best of them and would come back to you if I get any interesting result from my own research.