After reading online I see we have to go to London. Which is very inconvenient.
I don't think you have to go to London. You should be able do it in Edinburgh or Belfast instead
Can I apply when I go to the US, perhaps? We are flying back over in August of this year.
Despite not having trouble last time, it's actually illegal for a US citizen to enter the US on a foreign passport. You could have had problems with US immigration for not having their US passports.
I would definitely renew their US passports now/soon in the UK, before you fly to the US in August.
From the US Embassy website:
Can I hold more than one passport or nationality?
Yes. Naturalization in a foreign country, employment with a foreign government, and/or voting in a foreign election does not automatically jeopardize U.S. citizenship. However, please note that all U.S. citizens, even dual nationals, must enter and depart the United States on U.S. passports.