A lot of this depends on when you'll be flying (you mention May). If Chase runs the 100k promotion again in November, say it's December or January when you both have all 200k miles sorted out (made a purchase and completed a statement cycle, and spend $2500 within the first 3 months which then credits after you complete a statement cycle in the month that you spent the 2500th dollar).

If you're flying in the offseason you can get tickets for straight cash for not much more ($150-200) per ticket than the $550ish you'll pay in YQ (taxes/surcharges) for an award flight. So then it's not so worth it. You'll be saving the $200 but it'd be a better use of your time to pay out of pocket for the flights (you could use your card to buy them and earn even more miles) and use the BA Miles for another flight or AA domestic.

If you're flying in the summer, when economy fares from the west coast can easily be $1200 or more, and you book ahead of time so as to ensure there is award seat availability, then getting those tickets for only the YQ of $550 is a steal, saving your family $2600+ and keeping your costs to a minimum. In this case using BA Miles for transatlantic economy is an excellent deal and makes sense for your situation in particular -- especially if you make use of the stopover rule*.

Using BA Miles to book business/first is technically the more efficient use of the miles (a one-way ticket in business can run $8000+) but is not realistically efficient for some people (such as yourself, and me) because whilst you do get a better value "dollar for dollar" you still are spending more dollars and more BA Miles overall.

*the stopover rule allows you to use your BA Miles to book stopovers for the same amount of miles as a regular flight to that region. For example, for 50k miles you can fly SEA-LHR-SEA, or you can fly (for example) SEA-LHR-AMS-LHR-SEA and use the "stopover" as your time in each city.