Without knowing how long you have been feeling irritable most days, I would suggest you go to your doctor and get a medical check-up to rule out any biological issues. I would also suggest you seek individual therapy to begin working through your triggers.
You could read about the effectiveness of marriage counseling on Psychotherapy Networker.
Yes, individual therapy with the proper medication and medication compliance will greatly help your daughter.
Again, my condolences.
Yes, there is a lot of research/evidence that states therapy is successful in treating depression. However, the success of treatment is dependent on several things such as personal expectations, commitment level, and one of the most important is the therapeutic relationship you develop with your therapist. That being said, you would have to find what works best for you.
My mother has dementia, and is starting to forget my daughter. How can I explain this to my daughter?
I do believe there is help for you. Not knowing where you live, look into programs or therapists such as medical family therapy. Most often they can be found in hospitals. The program/therapists work with your doctor and a program doctor to set up the best treatment for you. They take your pain and need for the medication into consideration when working with you.