If this is your family in 1851, then I think I have found several of them in Tama County, Iowa in 1880. Hannah's John appears to be there too, so he definitely looks like a relative, but I'm still not sure whose son he is...
1851
Grange, Rhynd, Perthshire
John Swan, 56
Euphemia Swan, 49
David Swan, 14
John Swan, 12, Son, born Rhynd, Scholar
James Swan, 11
Mary Swan, 7
Peter Swan, 5
Here are the 1880 records:
Someone who looks like Hannah's uncle John is in Crystal Township, Tama County, Iowa. He seems to have just married his second wife, who was previously married to a McDowall.
Swan, John, 41, married, Farmer, born in Scotland
___Sarah F, 36, wife, married within the census year, Keeping House, born in Ohio
___Elizabeth, 15, Daughter (on the day of the enumerator's visit she was suffering from pleurisy), born in Scotland
___Adlaide, 10, Daughter, Attending(school?), born in Scotland
McDowall, James, 4, Step Son, born in Iowa
There are two households next to each other in Grant Township, Tama County, Iowa
Swan, Peter, 33, single, Farmer, born in Scotland
Johnsan, Marena, 54, widowed, Keeping House, born in Denmark
Swan, John, 22, married, Farmer, born in Scotland (on the day of the enumerator's visit he was suffering from "water in chest"

___Elisabeth, 20, wife, Keeping House, born in Scotland
McDonald George, 25, half-Brother, single, Farmer, born in Scotland
John's children in 1880 correspond to this couple in the IGI:
John Swan and Adelaide Lawson married 23 Oct 1857 in Perth, Perthshire
Children:
Jane Ann Keilor Swan 20 Jun 1860 Kinnaird by Errol, Perth
Elizabeth Swan 8 Dec 1864 Dundee, Angus
James Swan 13 May 1867 Dundee, Angus
Adelaide Swan 2 Jun 1869 Dundee, Angus
So Adelaide Lawson must have died either in Scotland or soon after they got to the U.S. Jumping ahead to the 1900 census, when John is still in Crystal, Tama, he says he came over in 1871-- he also has a third wife by then, who he married 13 years before, so poor Sarah F didn't last very long

In 1900 Hannah's uncle Peter Swan is still in Grant Township, still single, and still next door to George McDonald, who now has a wife named Hannah (born in Ireland). Both George and Peter came to the U.S. in 1868.
I've been trying to link the younger John Swan with George McDonald as a half brother and so far all my theories have gone up in smoke. For example:
In the IGI, the only Sep 1858 birth (which is what John gives in the 1900 census) is a John William Swan 10 Sep 1858 in Edinburgh
Father: John Swan
Mother: Helen Whitelaw
Another child to that couple:
Christian Fair Swan
3 Jul 1853
Ayton, Berwick
Their marriage was 13 Dec 1846 in Ayton, Berwick
On 22 Dec 1854 a Helen Whitelaw married Charles McDonald in Saint Cuthberts, Edinburgh. Her father was James Whitelaw
BUT, their only child in the IGI is Jessie McDonald, born 8 May 1855 in Edinburgh Parish, Edinburgh
And anyway, the timing is odd, since by their ages one would expect that George's father was the mother's first marriage, not her second (or during her marriage with John Swan

Oh well... any leads today in your research?
Regards,
Sarah