I just submitted my doctoral thesis yesterday. I finished my project two years ago and published it in a high level journal. My supervisor asked me to give the co-first author position to a postdoc, although there isn't any input from her. After a long time of struggeling, I agreed, because otherwise she will not support me in getting my degree smoothly and will refuse to write a recommendation letter for postdoc applications. After that, she still asked me to do many experiments. These experiments are for her funding, for other colleagues, and all not related to my project. She took four months to finish proofreading my thesis. Actual working time on it is not more than 24h. Now she asked me to come back for experiment after I start my postdoc training, otherwise she will not support me in the future if I want to find a scientist job.
She said she would not write me a reference letter if I didn't come back. Now I am leaving for postdoc training. So I want to know how important the letter is for a job seeking? Any advice?