I am looking for a pianist with difficult childhood. I would like to listen to his/her music and perform comparisons for my research. Is there a pianist you would like to recommend?
There is a distinction between pianists and composers - some composers of the period were also known pianists (e.g. Rachmaninoff), while pianists by trade are not necessarily also remarkable composers (classic exception is Horowitz, who wrote some minor compositions and made his own arrangements of other works). But if you are looking for someone with a difficult childhood, then some examples that came to my mind include Erik Satie, and Arnold Schoenberg. They were more controversial in their personality than was their childhood "difficult", however. But I guess the childhood must have had a role in their future career, wouldn't it? Satie was dismissed as a music student and in fact he was not technically superior to his peers. The fact that most of his music is simplistic (technically) reflects the desire for him to play his own compositions (to later contribute to the rise of ambient music and Dadaism). Schoenberg and other Jewish composers were brought up in the anti-Semitic atmosphere that permeated in the day. The composer also had a fear of the number 13, which affected his subsequent compositions. Growing up at the edge of tonality and the post-Wagnerian world, Schoenberg pushed tonality to the limits, so much so that he went over the border and, as everyone knows, became involved in the development of atonality - dodecaphonic music.
Those are only generalized remarks, I suggest that you read up more on them and discover more about how their early upbringing and start influenced their later development.