I’m not going to argue that GDP is a perfect metric, because it clearly is not. But I feel obliged to point out that 5/7 of the GDP created in your own scenario is a guy doing presumably valuable work, and 2/7 is the baby sitter doing previously unaccounted for work; which is also based on wages, perhaps more fit to their skills.

It would be great if we could measure work done without exchange of goods however that is generally not so large as to totally distort the general numbers. To no discredit of the work parents do.