Adrienne, thanks for writing and adding more information.
Also Thompson thank you for researching. Your response and help are much appreciated!
Now with the new possibility that Matilde could be Cherokee, I am liking this story a whole lot better. The Cherokee people originally settled in the American southeast, which is where Matilde's parents were born.
I think the Dawes Rolls begin in 1887? An earlier census of Cherokee people would help.
What was heard as "Kiowa" might be United Keetoowah Band of Cherokee Indians.
Adrienne, you write that your great-grandmother says "Matilda always told her stories of her being adopted but could not give any more information" since she didn't know her biological parents. This is consistent with the census records we found. Yes Matilde has her own surname within the Vanderpool household, so she may not have been legally adopted - but certainly she could have been raised by them as a permanent daughter rather than treated as a transient. Thus your great-grandmother's story and the records we posted fit well together.
About the laws re. adoption - you could research that separately. Probably you can't get expert help with that on this forum.