Having been a guest at Buck House a few times I can confirm Jordan's opinions of Her Majesty are completely correct, She is a very nice Lady and one of the best Monarchs we've had. She does love the corgis and has a passion for horses and frequently pops down to the Royal mews to groom the Royal mounts.
I wouldn't worry about the President's gift, it was the music on it and the technology behind it that expressed U.S. talent and craftmanship, not the container.
Her Majesty already has an example of U.S. Leathercraft, She recieved a pair of Cowboy boots during the state visit back in '72.
It's up you guys if you want to send something, but it should be done as an expression of freindship from U.S. citizens rather than an apology for the official gift. You wouldn't want Her Majesty to think you are still a bunch of rebellious colonials with no respect for authority would you?
If you do decide to go ahead you can find info on the correct ettiquette at the Royal website .