Excellent Jenn!
I just came back to the computer intending to post suggesting that Rachel ask for 1891 and 1901 lookups!
I had seen the following in the 1881 on FamilySearch and wondered if they were the right family (despite father being John):
8 Bedford St, Heigham, Norfolk
John S BARNES, Head, M, 36, b Eaton Norfolk, Seedsman Earlham Gardens? (Managing Assistant) (7/3)
Harriett E BARNES, Wife, M, 28, b Eaton Norfolk
Madeline Mary BARNES, Daughter, 3, b Norwich Norfolk
I guess not!!
Haven't managed to find a marriage for an appropriate Arthur and Harriett yet ...
Cheers,
JAP
PS (added later): The 1891 Arthur possibly the following:
BARNES Arthur Petchell, birth, Mar qtr 1860, Aylsham, Volume 4b Page 91