Leonard's death record gives his mother's name as "Elizabeth Miller" and her birthplace as Newton, IA which is Jasper Co IA.
John's father was George Smith. Elizabeth's was Thomas ______ (hopefully a review of Elizabeth's obit will be able to clear up her maiden name for you). Their first born son was named George Thomas Smith. Leonard's middle name was William.
Just a off side note: Elizabeth appears as "Elizabeth Myrtle Smith, wife" on John's WW1 draft registration. I have seen a submitted tree file that suggest her middle name was Lucille. Perhaps she has multi birth given names. My grandmother of German descent had three parts to her birth given name.
I briefly looked at 1880 census records and there was neither a Newton nor a Muellet that fit well. There was a Thomas Miller born Pennsylvania, wife Adelia born Iowa with a daughter Elizabeth born Iowa that was a potential.
To clear up and document for your family records you will want to farther research so that you have correct info whichever way. That's part of the 'fun' part of genealogy research...the more one learns the more one wants and 'needs' to learn even more. The 'hunt' can take one through many different records to gather as your documentation. The more you gather the more you'll realize that record to record, source to source can be slightly different. Partly why the more you gather the more accurate of a picture you will actually get of your family.
The very best of luck in your searches. And always remember that unless you are seeing an actual image of a 'record' or something like a cemetery tombstone, that you are getting other people's transcriptions which is not always accurate. Anywhere from handwriting is hard to read, to stones fade to human error.
You're on your way, just keep digging!