I had a look at the Swedish emigration DVD, EMIBAS and the only direct hit that I got on Ida Mathilda was the following which I checked at the online church books archives http://www.arkivdigital.net/
The family may have changed their last name after arrival. I know that you said that her fathers name was Charles (which more than likely would have been Karl/Carl in Sweden) but does anything else from the below match up with what you have?
Gränna AI:39 (1876-1880) Bild 138 / sid 638 (AID: v23600.b138.s638, NAD: SE/VALA/00106)
1876-1880, Uppgränna Frälsegård, Gränna landsförsamling, Jönköpings län, Småland
Sven Gustaf Andersson, b. 22 JAN 1847 in Adelöv, Jönköpings län, Småland
Married 13 FEB 1869 to
Mathilda Magnusdotter, b. 15 MAR 1851 in Gränna, Jönköpings län, Småland
Hulda Josefina, b. 31 OCT 1870 in Gränna, Jönköpings län, Småland
Anna Lovisa, b. 26 SEP 1872 in Gränna, Jönköpings län, Småland
Carl Rickard, b. 7 FEB 1876 in Gränna, Jönköpings län, Småland. Died 21 FEB 1876.
Ida Mathilda, b. 26 JAN 1877 in Gränna, Jönköpings län, Småland
Oscar Fredrik, b. 30 DEC 1878 in Gränna, Jönköpings län, Småland
The husband leaves Sweden without permission 10 NOV 1879 and emigrates to North America
Mathilda and all their children (except Carl Rickard) emigrates 26 OCT 1880 to North America
What do you think? If its not a match, do you have dates of birth for her father and siblings? That might help finding them.
Let me know and I'll have another look