Wow, I'm overwhelmed with the response! Thank you all so much for your efforts with this, there's a lot to go through! The effort from each of you is very, very much appreciated!
I will have to go through some of it over the next few days, but I think the mystery has been solved with Ethel Rose Dinger. Her father, Arthur Dinger, was my grandfather's brother. I believe this makes her my first cousin, once removed. That would definitely explain why she travelled to see my grandparents, who had migrated from England in 1911, in what was then the middle of nowhere!
I've attached the photo Ethel/Peggy with my grandparents, circa 1924. From left to right is Bill Hastings, Lilian Dinger (my grandmother), Ethel/Peggy, and Alfred Dinger (my grandfather).
I just wanted to reiterate how thankful I am for everyone's help. I have a lot of reading to do! I will make sure to have a look at every link you've all provided. Thank you!