Hi again, Tara,
Bummer about the marriage certificate not listing parents. Did they have to give their birthdates? Any witnesses to the marriage listed?
There's more than one way to skin a cat. Did you ever obtain a copy of her SD death certifcate? That's another document that could contain her parent's names. Fred MAY have been the one that signed as informant, and he may have known what her parent's names were and where in Germany she was born, plus her birth date 'should' be on there. You can buy a copy from the SD Dept of Health for about 15 bucks. The State File Number for her death is 97623, and you have her date of death and county.
Another angle - find an obit in a SD or IA paper as 'LHSwisher' pointed out earlier. A quick search on the 'net indicates at least 2 public libraries in Roberts County; 1 in Sisseton and 1 in Wilmot. You may be able to e-mail, write or call them for help on obtaining old obits (and what papers were in circulation back then (1925).
Might want to check Pocahontas, IA libraries also for help with obits - there may have been an obit for her there as that's where they lived for so long.
Also, post queries on the boards here for help with obits in those specific counties. [Go to the message boards and post in the state and county boards and ask for help with an obit.] Some members here are willing to help other members and check their local libraries for obits for you as some of those old papers are on microfiche. You know when and where she died, and that makes it easy for them to search.
[Plus, somebody posting there may be related to you somehow. You can also post under the surnames boards.]
Some members here also volunteer to check local cemeteries for you for graves and burial records. And that's another possibility - checking with cemeteries about burial records (and mortuaries for burial prep). Somebody in SD prepared her body for a funeral and burial, and somebody [mortuary] in IA actually buried her, and there should have been a record. Some, but not all, cemeteries have birth date, spouse(s) and parent info as part of their records, and maybe even lot owner.
Been to Find-a-Grave? There's some memorials to some of your Barnhardt's posted on there. There's one there for Fred, Fred's sister - Mary L [Barnhardt] Christensen, their parents, etc. If you didn't post any of them, you may want to contact the people who did (via e-mail thru that website), and ask them for any info they may have; some of them are probably related to you and may know more.
Did you find that passenger list I found? [Hey, I'm still learning too; you gotta start somewhere, and you'll keep learning.] So, now you need to find a way to confirm (or deny) that that's your Emma. One way to do it would be to figure out just who this "Carotens Terlefs" is. [Whenever you find something here at Ancestry you're not quite sure about yet, you can always just save it to your 'shoebox' so you can reference it again easily. You can always delete it later if it turns out it's not right.] It's scribbled above her name on that list - niece. Looking at "Carotens" age (66), seems to me like this guy would more than likely be a great uncle - the brother of one of her grandparents - just speculating here.
I took a look at your tree, and I see that Fred's mother's maiden name was Lange, and that you have his father's mother's maiden name (Fred's paternal grandma) as (Catharina Margaretha) 'Dethlefs', and that these folks were in the Holstein area.
Back to the 1925 Iowa Census, and Emma's mother's maiden name - "Delaffaf"...hmmm...wonder if they were saying/writing "Dethlefs". DON'T KNOW! But, what I did was search German records at FamilySearch.org and guess what? Yeah, there were some Dethlefs/Dethlofs, etc. in that Holstein area and some married a Lange or two. Common back then for families to marry into each other. Just something to look into and keep in mind.
Yes, getting Emma's birthdate and more confirmation of her mother's maiden name would help a lot. Also, what part of Germany she was from. Keep plugging away, you'll eventually get a lead.
How long have I been researching my ancestors? Three years now; never set out to do this - just stumbled into it and now I'm determined to see it through as best I can. It's fun, but it's 'work' too. It don't come easy sometimes. :-( I've got mistakes on my tree, and I know it, and I know where they are. I've got a few major brick walls of my own also. Been searching hi and low for 3 years for my 2nd great grandmother.
Do the same, just keep searching; more records are always coming online too. Contact others that are searching for the same family lines.