The only thing I can think of that might be related is my grandmother's saying "the weasel's waiting". The use of the word "weasel" referred to the weasel on a spinning wheel. This is the large wheel which is revolved by the spinner in order to measure off thread or yarn after it has been produced on the spinning wheel. So when my granny said "the weasel's waiting" she meant "it's time you got to work so hurry up". So maybe your mother's saying "jig the weasel" also has something to do with "hurry up and get to work because the spinning wheel is waiting". Just a shot in the dark here, but it might be from the same "spinning" source.