In 1910 both George & Euphemia say they came over in 1870

Still need to find a trace on the passenger lists-- difficult to be sure since the lists from that far back don't give much information and there are too many George Youngs.
Euphemia and family are easier to find. They came over on the Britannia arriving May 26 1865. Jane was with them, so she must have died in America. The children are Euphemia, James, William, Jane and Richard. Wonder where John who was 8 in the 1870 census was? Anyway, it is clear that the other children, those born in the U.S., were not Francis and Jane's, with the possible exception of wee Francis, who was not born yet when they came over.
Are you interested in the fate of Euphemia's family? Her father, stepmother and some siblings went back to Iowa (I say "back", since most movement in the U.S. is east to west, and it is odd to see the reverse at that time!). They are all coalminers in Machacinoe Settlement, Mahaska County, Iowa. I can go on with them if you like. In fact... I think I'll fast-forward to 1925 in the hopes that wee Francis is still in Iowa, since the 1925 Iowa census gives the names of the parents. No such luck. Only son James is still in Iowa at that time. He gives his parents as Francis Chambers, born in Scotland, and Jenna Smith, born in Scotland.
Cathy's advice about the Historical Museum is very good. Often the Historical Societies in such towns have a wealth of information, and they are usually very generous about sharing it!. I'd also check out the Sweetwater County, Wyoming GenWeb:
http://www.rootsweb.com/~wysweetw/
Lots of good stuff on that site!
All the best,
Sarah
P.S. On the RootsWeb site there is a cemetery link. I see that Euphemia died 29 April 1917 and George on 11 Nov 1915. There are other family members buried there also.