The accounts that support the story are anecdotal in nature and do seem to have discrepancies, but no doubt have some basis in reality:
Ulysses Jr. (Buck) in a
San Diego Daily article in 1922:
"The saddest I ever saw my father was when my sister Nellie was married. It was a lavish White House ceremony and she married a foreigner. He was very downcast for a long time about it. That evening I found him sitting with mother upstairs in my mother's dressing room and he was sobbing like a boy. I was so in awe of my father I couldn't think of what to say, so I withdrew, deeply shaken."
White House worker William H. Crook (from
Through Five Administrations 1910):
"After his daughter had left the house on her wedding trip the General was missed. After considerable search he was found sobbing in his daughter's room, with his head buried in her pillow."
Jesse Grant (Son) from
In the Days of My Father, General Grant 1925:
"[President Grant at the ceremony was] silent , tense, with tears upon his cheeks that he made no movement to brush away."
I think it's safe to say from Grant's own correspondence at the time that he was reluctant about the marriage. He thought his daughter too young to marry and did not want her to move away. He tried to encourage Algernon to become a US citizen and for the couple to settle in the U.S..
Grant wrote Algernon's parents in 1873:
"It would be with the greatest regret that I would see Nellie quit the United States as a permanent home...May I ask you therefore...whether your son expects to become a citizen of the United States?"
Algernon's older brother died in the fall of 1873, making Algernon the heir to the family estate and essentially ensuring him and Nellie would be moving to England after the wedding. The emotion Grant exhibited was undoubtedly tied to the realization that his daughter would be moving abroad, a very difficult reality for any parent of an 18 year old to handle. The marriage of course did fail, Algernon died in 1893, and Nellie moved back to the states and eventually remarried.