Has anyone seen an object in the night sky the same size as the moon along with our moon?

What you probably saw were "dumps" from spacecraft. Spacecraft and satellites frequently dump excess fuel or water which rapidly expands in the vacuum of space and forms large clouds which are lit by the Sun, even though it's below the horizon for the observer. I've never seen one of these personally, but a friend of mine has observed them several times. The fact that you are in Kentucky puts you "downrange" from the Kennedy Space Centre in Florida, and makes you much more likely to see such things.