Sounds like she is dealing with depression. It's not only feeling sad all the time. A very common symptom of depresison is anger about everything, or in situations where most people wouldn't be angry. Urge her to see her MD right away - they can start her on a SSRI type drug that will bring her serotonin levels to a more normal place. It helps people deal with these emotional extremes - which is typical of depression.
She needs to run - not walk - to the doctor and tell him/her about this. She should do this for her child if not for herself. People have all these preconcieved ideas that antidepressents are for weak people, or "someone else" - but they are a miracl drug on the same level of insulin, antibitoics, etc. My MIL suffered from depression all of my husband's life - she did not know how to deal with her extreme emotions and myhusbnd suffered for it and it only now, at age 43 beginning to really recognize and deal with the effects.
Give her facts about depression such as: depression affects millions of people, it's usually NOT permanent, medication can often jump-start a person's body into producing serotonin & the body takes over, depression is not just sadness, it includes extreme emotions, disproportionate responses, inability to enjoy things that you used to enjoy, changes in sleep (needing much more or much less) changes in eating/weight, etc.
If she really loves her child she will do what her child needs her to do. If she was a diabetic, or if she had strep throat or cancer, wouldn't she take medicine and do what she needed to do to get better?
Finally - wholistic approaches: fish oil, exercise and prayer.