So not only do YOU have to deal with a demanding job, divorce, move, new baby, death in the family, etc., your child is putting even more stress on you by freaking out. It's dadgum tiring.
So here's what you do. Get them a lovey - a special toy, stuffed animal, or even the shirt off your back. They need an object to help them with the anxiety.
We recently bought a new home and my youngest daughter was having trouble with the change. So while shopping with Daddy one day, she ran across a duck that she fell in love with. At first my husband thought, "No way am I getting her that duck!" I mean, really. I had just packed up three large boxes of stuffed animals - do we seriously need one more stuffed thing to keep up with??!! But to her, this duck was special. And knowing that she was having a hard time with our move, my husband changed his mind and said, "You know what? I think this duck might help you feel better about moving!" And thus, "Moving Duck" was adopted. She now has him with her at all times and we haven't had a whimper, whine, or sad face since.
Now granted, we have a strong family bond and she has two older sisters to take care of her and show an example of confidence in our move. That helps tremendously. You must have a solid foundation of trust, love, and attention - no object can replace that. But when you are crazy busy and have your own issues to deal with, help them along with a lovey. Train them how to turn to the lovey when they are feeling anxious, sad, or angry. They need a way to channel that negative energy and give it up to something soft, squishy, and hugable. (Although I've seen a favorite army-dude action figure work just as well!)
Remember to give lots of hugs and kisses, and project a loving confidence in your decisions or an appropriately stable attitude in times of grief or stress. It's totally okay for you to be sad or upset - just teach them how to cope by your actions. They learn by example!