Upvote:2
My USA passport expires two weeks after my planned return from a one week trip.
I understand this to mean your passport is valid during your trip.
As long as the midnight has not passed on the expiry date, your passport is valid and you will have no problems entering the country.
Even if by chance you extend your trip and your passport expires, the US embassy can grant you an emergency passport to return.
As far as entry to Dublin is concerned, as US citizens do not need a visa your passport is only used as proof of your citizenship.
For your trip to the UK, you do not need a visa (unless you have been previously denied entry) so you should not have any problems there either.
Of course, for travel within the US you only need to show government issued identification and you don't require a passport at all.