1930 US Census in Sheboygan, Sheboygan, Wisconsin shows 20 yr old Carl living with parents James (51) and Lena (47) both born in Holland arriving this country 1899. 1920 Census is consistent with 1930 but add parents were naturalized in 1910 so you may be able to find that record. 1910 (April 20th) Census shows 1 month old Charles so approx birth date is March 1910. James, the father, was a widow in the 1940 Census. It looks like Carl had two brothers and two sisters. Possible arrival record for Jacobus Dommisse (age 20, laborer) from Nienndorp or Nienndorf, Holland, at Ellis Island on 14 May 1899 on the ship Statendam out of Rotterdamm. Destination shows Sheboygan, Wis. going to join friend C Buleyse (Sp?) in Sheboygan. Looking at the various pages, it's not clear to me if ship arrived the 4th or the 14th so look for both. I don't see Lena on the list of passengers. There are two women named Lina, both from Hungary. I can find no place in the Netherlands with the name of Nienndorp or similar. WW I draft registration card for James gives birth date as 30 Mar 1879, medium height, medium build, gray eyes, brown hair. I see there is a naturalization record for James Dommisse but I don't have a paid Ancestry.com membership so I can't see it.
There is a Carl Dommisse (age 57) living in Sheboygan who registered for WW II draft with birth date 18 Sep 1884 giving birth province as Zeeland, Netherland. I suspect this is James' little brother and your Carl's uncle. So Nienndorp (or whatever) is likely in province of Zeeland.
Find a Grave shows James died 27 Sep 1961 and is buried in Wildwood Cemetery in Sheboygan. Same site shows Lena Roelse Dommisse born 30 Aug 1882, died 8 Apr 1939 and her mother was Catherine Roelse (8 Nov 1851-22 May 1933) also buried in Wildwood Cemetery.
My wife has a Kornelia Dommisse (b. abt 1788 in Oostkapelle, Zeeland, Netherland) in her family tree and also a ton of Roelse from same general area whose descendents emigrated and lived in Sheboygan County. However, I don't see a Catherine Roelse. I'm sure there is at least a distant connection.
From this, I'd say that Carl's mother (and James' wife) Lena Dommisse (nee Roelse) was actually born in Wisconsin. Googling Lena Roelse I found her parents were Adrian Roelse and Katharine Sanders. This record on Ancestry also states she had six children (not five).
I see a marriage record for Jannes Dommisse (probably transcribed incorrectly) and Lena Roelse on 18 Dec 1901 in Sheboygan, Sheboygan, Wisconsin. Groom's parents are Jacobus Dommisse and Janna Vandalen. Bride's parents are Adriaan Roelse and Katharina Sanders.
In 1900 US Census for Sheboygan, Lena Roalsa [sic] was enumerated living with parents and sister Fannie. Birthplace shows Wisconsin. Parents Adrian (b. May 1854) and Catharine (b. Nov 1852) in Germany. Birth place for parents is wrong. Idiot enumerator didn't know the difference between Dutch and Deutsch! Father arrived this country 1881. Father's occupation is white washer. Both sisters are varnishers in a chair factory.
I see that there is a place named Nieuwdorp in the province of Zeeland, Netherlands and it's near where the Roelse and others in my wife's Dutch ancesters originated (Westkapelle). Looking back at the manifest for the ship Statendam I can see that Jacobus (which is James in English) Dommisse was from Nieuwdorp!!!! So, you are on your way with both of your Carl Dommisse's parents. Best of luck. You can contact me, Paul 503dash682dash0599 if you have questions.