I wouldn't contrast Dwarves as children of Aulë vs. Elves and Men those of Ilúvatar since no contrasting against Ilúvatar in such a context is ultimately possible. The Naugrim are in several places actually referred to as the "adopted children of Ilúvatar" because it was He who gave them true life. What Aulë initially made were like puppets with no free will of their own. In the lengthy discussions on the nature and origins of Orcs, Trolls etc. (especially in the 10th volume of History and also in letters, but definitely elsewhere too) this nature of Dwarves is referred to. In a similar sense, some Elves' naming of Orcs "children of Melkor" is dismissed.
I would instead emphasize their being of a different "species" with distinct anatomy (consider the virtually identical appearance of males and females), which renders it impossible for them to unite and breed offspring with Elves or Men. (Different yet not too remote...)
Landroval: Kibilturg, Taurunion, Erohtar... (Watchers of Elendil)
Crickhollow: Kibilturg (Tarciryan Knights), Zigilturg (Forever Notorious), Birnavor (The Northern Kingdom)...
Visiting elsewhere as Kibilturg, Urwendil... Born and raised on Imladris