In order to combine these two sentences in the best way, you need to make sure all of the information from the two original sentences is presented into the combined sentence. Also, the words set off by commas, need to be describing the correct words, which shows they are in the correct spot. Considering all of these, the best way to combine these would be:
Grandma Ellis, a native of Ohio, grew up during the Great Depression in the 1930s.
This is the only sentence where the appositive is used correctly.