First, you may want to add some context to your post: in THE FOG, Adrienne Barbeau's kid asks, "Mom, can I have a stomach pounder and a Coke?"
Is it really a mystery? It sounds to me like it's a play on "quarter pounder." Whatever it is, it's surely just a generic phrase for the kid wanting junk food without naming an actual brand.
I've met Adrienne a couple of times and never thought of asking her. What are the odds that she'd even recognize the line?