Place of birth (in the database): Västerhejde Gotlands län
============================ 1890 Swedish Census CD:
Nilsson, Karl Peter Fredrik eldare
b. 1864 i Västerhejde (Gotlands län, Gotland)
Gröndal köpingslikt område Döderhult (Kalmar län, Småland)
Place of birth (original source): Vest. Hejde Wisby l.
1900 Swedish Census CD:
Nilsson, Karl Peter Fredrik Eldare
b. 1864 in Västerhejde (Gotlands län, Gotland)
Å församlingen skrifne Oskarshamn (Kalmar län, Småland)
Absent when registering
Place of birth (original source): Västerhejde Gotlands län
There are more than 100 possibilities for Mathilda Andersson on the Emibas CD, which is only about 75% complete. Try to find more information.
Download the booklet "Tracing Your Swedish Ancestry" for your parents and also for you. It has hints on how to try to gather clues to find the parish in Sweden. This url has a link to download that booklet.
Family History Centers have access to Arkiv Digital which has scanned Swedish parish records which should help with Carl Petter Fredrik, but you need much more information to find Mathilda.
Try using the Swenson Swedish Immigration Research Center. They are very popular, however, and there is a waiting list. Don't wait too long to contact them. If you go there, be sure to make an appointment.
Also try to find a more complete birthdate for Mathilda and look in the censuses for 1900-1910-1920-1930 to look at the column for a year of immigration. (I don't yet know if 1940 has that immigration year column.) You will also find a month and year of birth in the 1900 census.