I think this isn't as clear cut as some may assume.

I can see a BA fare DUB-NYC//IAH-LON-DUB for £900 in late August. Kayak has a good search facility.

So that's £2700 plus £200 to get to Dublin and stay overnight. £2900

Or, use the miles, pay c. £1k in charges then buy another ticket, which I think will be about £1600 as I think the child will get 25% off.

So even if you value the miles at 0.5p each, you're paying a £200 premium to fly nonstop, plus foregoing another £200 worth of miles.

With kids (I have three of them) I would always look at the nonstop options.