Hi Bob...
I don't have kids, but your story made me think of a costumer I'll call Matilda. (No, this isn't me... just someone I know of.) Theatre costumers are notoriously short tempered because they are notoriously overworked, understaffed and underbudgeted and always on a deadline. I don't know many that have not abused stimulants at one time or another... which adds to the grrrrrr factor. Matilda was a dragon of the most fiery sort... but she had a heart after all, and realized she was upsetting the people she cared about... as well as those whose help she needed. So Matilda pulled a brooch out of stock... a bird. When the bird was flying upright, one could approach Matilda and expect civility. When the bird was upside down, Matilda had determined that one more thing would send her off the deep end. No one wanted to be the one more thing, and it was nice to have the warning. It also added some humor to the situation.
Even a 7 year old should be able to understand about respecting your work space. Perhaps there could be an "I'm working intently now" symbol that alerts the kids to be quieter, or to not interrupt you. After all, they wouldn't be able to call you willy-nilly if you were in an office working for someone else. Sometimes it has to be "office time" or nobody eats. I just hope you're also able to make some "us time".
Love,
Smoke