I am sorry to hear about your negative experiences with the mental health system. I am unsure about why you are getting such reactions from mental health professionals. I am particularly disturbed to hear that your psychiatrist replied that he was unavailable until March after you sent him an e-mail about your intention to end your life. It is also shocking to hear that your psychologist did not feel the need to see or help you immediately. I do not have an explanation for their unethical and unprofessional behavior.
With regard to your pastor, he may have been trained (as are most mental health professionals) to call for immediate help if a person is vocalizing their desire to end their life.
Not all mental health professionals are specifically trained to deal with clients in crisis. He or she may not feel comfortable or confident in their ability to help someone with suicidal thinking. Another explanation may be that you very frequently send them these types of messages and they are not taking your calls for help seriously. No matter what prompted their reactions, the way in which they responded to you is inappropriate.
Many people believe that ending their life will end their suffering. The truth is that you do not know. No one knows what the afterlife holds, or if there is even an afterlife to speak of. Suicide may not bring you peace at all. It may have the opposite effect. No one knows.
If you took your own life, it would have an extremely negative effect on the lives of your children and loved ones. Your children would be left in this world motherless. What would happen to them? Who would raise them? What would they think about after they learn that their mother has ended her life? Children who have parents who commit suicide have a greater risk of suicide themselves. This means that your actions could increase the likelihood that one or both of your children would someday take their own lives. They are other ways of handling your pain and suffering and I strongly advise you to consider them.
You already have one year of sobriety. This is a remarkable feat and I hope that you take time to praise yourself for this effort. You should consider finding a new psychologist or therapist who will not ignore your calls for help. A good therapist can help you end your pain and suffering and bring you back from suicidal ideation. Your children need their mother so please do try to find someone that you like and trust to help you decrease your everyday pain and desire to end your life.