You appear to have properly interpreted
Tolkien’s poem “The Little House of Lost Play”.
The concept is that children of
Men can through dreams visit the Lonely Isle in the west by
Valinor, and play in their dreams in a cottage and its environs which have been set aside for children who come there in dreams. The language of the other children which the two protagonists do not understand would be
Elvish, I believe. The two children may have been originally intended to be J. R. R. Tolkien (the fair child) and Edith Mary Bratt (the dark child) whom Tolkien married.
The conceit of the poem may be that Tolkien originally met his future bride in dreams when they were young children and later rediscovered one another when they were almost adults, after they had become too old for these dreams.
The poem is referred to in “The Cottage of Lost Play” , chapter I of
The Book of Lost Tales, p. 19, as “a song among Men” .
Tolkien later rejected a concept so twee from his legendarium. Tolkien, in 1971, remarked on his poem “
Goblin Feet” (see
http://ladyaleta.com/aleta/tolkien.htm ) written about the same time: “I wish the unhappy little thing, representing all that I came (so soon after) to fervently dislike, could be buried forever.”