I would go direct *unless* that £500 would get you a seat for the youngest you aren't paying for now. In that case, not having a lap child would win out over going direct, assuming the same airline. There are some airlines (looking at you American Airlines) I would pay more to avoid.
I only have two kids, but I have flown alone with them indirect multiple times thanks to parents who live in places that cannot get direct flights from the UK. The most ridiculous one was Boxing Day last year, when we stayed over in Chicago and got a crazy early flight the next morning to save £500.
I only have two kids, but I have flown alone with them indirect multiple times thanks to parents who live in places that cannot get direct flights from the UK. The most ridiculous one was Boxing Day last year, when we stayed over in Chicago and got a crazy early flight the next morning to save £500.