Kevin,
That adapter is very cool. It would solve the problem for plugging into the trailer outlet.
Uncle Chan,
If you still want to change the receptacle on the power cord this site might help with the wiring. A 20A receptacle on the cord can still be used with 15A plugs. The additional feature is that it will accommodate the sideways blade in your power inlet.
http://assets.twacomm.com/assets/pdf/17391.pdf
The link contains pictures and simple diagrams. The outlet slots marked "W" mean it is for the common wire (with white insulation) and the one not marked is primary. Some of the diagrams are for 250V items and do not apply to us.
This can really confuse me because things are turned around between receptacles and plugs. Regarding receptacles, if the ground hole is turned downward, the 15A one has two vertical slots with a longer slot on the left and that is the common. The shorter slot on the right is primary. This is residential wiring except the ground hole may be turned upward instead of down in some houses.
A 20A receptacle with the ground hole downward has a T-shaped slot on the left and a vertical slot on the right. On this one the T-shaped slot is the common. It is in the same relative position as common on the 15A receptacle. If a 20A plug has a blade turned sideways it fits into the T-shaped slot and is the common.
Bill
PS A page similar to the one in the above link helped me a lot with AC wiring. I carefully marked all the blades and slots and still managed to reverse common and primary on one receptacle. A plug-in circuit tester like this detected my mistake and it was easy to correct.
http://www.tripplite.com/en/products/mo ... delID=3941