First, you need to know if she was married before or after immigration.
Since you know the date of her second marriage in the US, you should look for US Census records around that time. My great grandfather was a Danish immigrant, and on the 1900 US census, there's a column indicating the year of immigration:
In his case, it says 1892. You can then search The Danish Emigrant Archive to see if records of a person with the same name leaving the country exist.
To use my great grandfather as an example, I was able to confirm that someone with his name left in 1892 by searching that database. It also says his destination was Detroit, Michigan. He lived in Michigan, so there's the double confirmation.
Note: My great grandfather had a drastic name change between Denmark and the US. "Lars Jørgen Vilhelm Mortensen" changed to "William Mortensen", how I figured that out is beyond the scope of this question. Knowing his Danish name was a prerequisite to use this database.
So, here's the good news! "Milling" is not a Danish surname, so it's very likely that you won't encounter the typical clutter of people with the same name if she was already a Milling when she left Denmark.
Since her last name is so uncommon for Denmark, the whole US-census-checking step is unnecessary in this particular case.
Simply searching "Milling, An" returns this. You can see if you do the math on the presentation date and age, you are within +/- 1 year of the birth date you have in your question. Also she is headed to Illinois where you know she married/lived in the US. Based on that, I suspect this is her record of departure from Denmark:
So, the "Anton Milling" record that came up is a coincidence, but I checked all "Millings" leaving Denmark in 1907 and they are the only two. Maybe they are connected? They both left Denmark to both go to Chicago the same year. Coincidence? Maybe. However, if you look at the birth locations for them, he is born a short distance south of Nørresundby where Anna was born. So I would make a note of this man and put it in my back pocket for later.
Now that you're equipped with her...
Full name: "Anna Eleonora Kirstine Pedersen Milling"
Birth town: Nørresundby, Nordjylland, Ålborg, Denmark
Year of departure from Denmark: 1907
I would search for records around Ålborg/Nørresundby for more info.
Still not convinced this is her? Okay, so now that there's a sturdy hunch that she left Denmark as a Milling, let's look for a US census record to corroborate a 1907 immigration... I searched Familysearch.org for Anna Milling. There's a 1910 census from Illinois with a Danish woman named "Annie C Milling" - Americanization of names is extremely common. That census indicates an immigration year in the same manner as the 1900 US census for my great grandfather. Side note - this census says she is single.
Guess what? It says 1907. It also says she is 22 years old, which closely agrees with a 1887 birth date. It also appears to indicate that both of her parents were born in Denmark. - This is useful.
Okay, so now you have a double confirmation that the woman leaving Denmark in 1907 is her. To find her Danish records, you'll need to use the Danish version of her name. You seem to believe she was married twice, so let's fix the name:
"Anna Eleonora Kirstine Pedersen Milling" becomes "Anna Eleonora Kirstine Pedersen".
Another FamilySearch.org record search for this name without Milling yields an 1890 Danish Census for a Nørresundby-born "Ane Eleonora Kristine Pedersen" living in Ålborg, Denmark.
Ancestry.com yields an April 6, 1902 confirmation record that indicates her birth date is December 12, 1887 not 1888. (Also Ålborg)
Additionally, I found the actual birth/baptism record itself, which confirms the birth date of December 12, 1887 as well. That is actually an even closer match to the emigration record above in which my math yielded 1887 as her birth date.
Anyway, to keep it on topic, you want to know when she married the first time.
Unfortunately, that's where the paperwork dries up. One thing I can say, since we know her confirmation was in 1902 and she left Denmark as a Milling in 1907 the marriage happened between 1902 and 1907 since they did not typically get married prior to confirmation. I don't want to speculate about why she was single 3 years after leaving Denmark if she was married in 1907. Another option might be to seek a US divorce record between 1907 and 1910.
To summarize your questions:
- "I want to track down her other last name: "Milling" perhaps mis-spelled."
According to the emigration record, this is the correct spelling.
- "Was she married in Denmark before immigrating or married in USA?"
She appears to have emigrated (left) Denmark as a Milling, so if this is a married name, then she was married in Denmark between 1902 and 1907.
- "Who was she married to?"
I am unable to find any information to confirm
- "Any children from that spouse?"
Again, unable to confirm 100%. Probably not though because she wouldn't have left small children (<5 years old) in Denmark and have gone to the US alone and been single (per the 1910 census).
A final note of pure speculation. Anton Milling, who I stumbled across in the emigrant database has records of him passing through Vermont on the way to Chicago. The notes say he is going to meet his, "friend, Christen Petersen".
Could "Christen Petersen" be referring to "Anna Eleonora Kirstine Pedersen"? Maybe he was just her boyfriend? Maybe he was just a friend and they lied about being married to help her immigrate somehow? Another possibility is that he was some sort of legal guardian or adoptive father.
Remember, she left a few months before him, so that would add up that he would be on his way to her and not the other way around if they did know each other.
The passenger list from Vermont says "Friend Christen Petersen, 650 Clairemont (or Claremont) Ave." If you can confirm whether Anne lived at a 650 Clairemont (or similar) address, I think you can safely assume this man would be her first husband.
If you have doubts about Americanization of names. Remember, my great grandfather went from.
"Lars Jørgen Vilhelm Mortensen" to "William Mortensen".
He immigrated at the age of 24 and lived to be 84. Over those 60 years, only one lone us-based document used the name "Lars" after he left Denmark. Jørgen was to never be seen again, and Vilhelm was always written as William.
Good luck in your searches.