Space Twins on the Moon is another Christian book I have found about a fictional trip to the Moon.
James C. Hefley. Illustrated by Robert F. Smith. Space Twins on the Moon. Cincinnati, Ohio : Standard Pub. Co., (96 p.) 18 cm. 1971.
A family is invites to live on the Moon for a Month.
Note that they were invited because the Glenns and Bormans were also Christian so they are "perfect examples for all Americans to consider." They would be helping helping to explore what an extended stay on the Moon would be like for the families of the scientists.
"...the [Russians] would probably have said that they had come to the Moon and couldn't find God."
Basically they come to the Moon, have a few adventures and because one of them is injured they just head right back to earth.
More of an oddity than an important children's book but it shows how the "race for the moon" got into all sorts of stories for children.