I devote this poem to my mother- Incorrect. I dedicate this poem to my mother- Correct Devote: (1) To give all of something, especially your time, effort, or love, or yourself, to something you believe in or to a person. (2) [passive] to use a space, area, time, etc. for a particular purpose. Example (1): He left government to devote more time to his family. Example (2): Over half his speech was devoted to the issue of unemployment. Dedicate: To give all of your energy, time, etc. Example: He has dedicated his life to scientific research. Devoted is more likely to be used to talk about family or loved ones (WITH EMOTIONS) whereas Dedicated is used to talk about work or other interests (MORE ABOUT COMMITMENT). (Source: http://ielts.studyhorror.com/questions/dedicated-and-devoted/58)

Devote implies ongoing action (devotion of one's time or resources to accomplish something); dedicate means to set something aside (often a person or inanimate object) in honor of something or someone else. There may be some instances where they can be used interchangeably but they do have slightly different implications.

Both of them can mean to commit time and effort, or loyalty, to someone or some purpose. "He devoted his life to music." "He was devoted (committed) to his wife." However, you can honor someone by acknowledging them in some poem, book or gift. "He dedicated his book to his wife, Jane." = In the front of his book, he wrote "Dedicated to my wife, Jane" It can also be in memory of someone who has died. "He dedicated the poem to his late father."