I have made an assumption that this wife and two children in the census data belong to this particular Paul Remington. His age and birthplace agree, and since he moved to MN with his mother and stepfather, this makes it more likely that he later moved to ND.
In the 1900 Federal Census, Paul & Odessa and their daughter Elizabeth are living at Bismarck, Burleigh Co., ND.
In 1910 the family is still at Bismarck, Burleigh Co., ND. There are now two children: Elisabeth & Paul Jr.
In 1920, Paul, Odessa, and Paul Jr. are still there.
In 1930, Paul & Odessa are still living at Bismarck. Son Paul is married and living in the same town.