If "you" know specific information about Ida, but you decide to keep that information secret from those who are trying to separate your Ida from many thousands of others Idas with the same name (because you already know that information), then how do you expect helpers to find her ancestors?
We are not limited to information from our families when we do genealogy. ;-) There are places to search for more clues. Any public library should have books on genealogy for you to check out.
When was she born? U.S. censuses provide an age which can be used to estimate a year of birth. The U.S. Federal Census provides a month and year of birth. Death certificates provide a date of birth and (if you are lucky) a specific place of birth. Marriage applications provide an age and sometimes a place of birth or names of parents or both. Obituaries sometimes (especially in rural areas and small towns) have a great deal of genealogical information, including when/where someone was born, parents, siblings, etc.
Since Ida lived until 1901, you can find the month and year of birth in her 1900 U.S. census record.
Where was Ida born? The U.S. censuses provide a state or country where a person was born.
If she was foreign born (Sweden?), then the 1900-1910-1920-1930 U.S. censuses provide a year of immigration.
If she was U.S. born, then look at the censuses during her lifetime to see who her parents were. (The 1890 census burned so the next census working backwards was 1880. Censuses were taken every ten years (federally). Some states had state censuses taken in-between the federal censuses but Illinois stopped state censuses in the 1860s.
When did she marry Peter Alfred? I don't see any Ida Carlson marrying a Peter Johnson but perhaps this is the right man using Alfred. I looked on the Illinois Marriage Index.
JOHNSON, ALFRED CARLSON, IDA 1888-07-06 2 227 3963 LA SALLE
I looked on the pre-1916 Illinois Death Index and couldn't find the 1901 death of an Ida Johnson in Henry County, Illinois (where Opheim is located). There are a few Ida Johnson deaths in 1901 on that index, however.