You sound a lot like my mother. She suffered from severe depression and anxiety and would lash out at myself and my siblings. She got help with therapy and medication, so she is doing significantly better now. Definitely find yourself a therapist who you feel understands you. They should not doubt your feelings. I have enough anxiety to get in the way of living normally and I was denied treatment from a psychiatrist who insisted I could not have anxiety because I /wasn't harming myself./ Needless to say, he didn't work out. You sound like you do have a lot of anxiety and maybe a separate panic disorder along with your depression.
To get better, you MUST see a psychologist, just not necessarily the first one you see. I have had two psychologists who worked for me. My old psychologist was just someone to talk to and offer advice, but my new psychologist has a different approach, cognitive-behavioral therapy and setting goals to reach one at a time. This works for me as well. Find what and who works for you. Maybe even try group therapy. As someone with very severe social anxiety, I can tell you from experience, it's not as bad as you think as long as you find the right group for you.
Even more importantly though, go to a psychiatrist. Vitamin D and magnesium might help you, but they aren't made specifically to treat mental disorder. After my bad experience with a psychiatrist, I was terrified of taking medication for fear that I would end up hurt. But again, it turns out you just need to find the right psychiatrist, someone who listens to you. Getting the right medication is trial-and-error, but the chance that it helps you remain in control is SO WORTH IT.
A side note: yoga is a good idea! If you don't like it, try some other form of exercise. Exercise helps. Eating healthy also helps, but I don't recommend trying it if the hope for an unhealthy treat after a hard day helps keep you going. Maybe try avoiding foods that cause inflammation? Inflammation in certain parts of the brain has been linked to emotional disorders in some instances, so it's worth a shot.
Please at least keep trying, if only just for the sake of your children. Good luck finding the right treatment for you!