If they were married 18 years by 1900, and she arrived in the US in 1882, they must have married almost immediately. (One census says she arrived 1881, but the immigration record you have attached definitely says 1882 -- and that she was Kibble on entry to the US.)
So it is definitely in the US you should be looking.
1910 census says they were living with a daughter (Margaret) and son-in-law (William) - and it looks as though there is one grandchild (William) also listed. If you have a date of birth for the daughter, it might help find the marriage date.