Just in case you don't have this entry, here is Alice with parents on the 1871 census in Harrietsham:
ref RG10 947 folio 26: The Bell Inn Harrietsham
John Butler head mar age 50 Innkeeper and farmer of 15 acres employing 2 men born Boughton Malherbe
Alice do wife mar age 38 born do
John do son age 16 innkeepers son born do
Jemima do dau age 14 born do
George do son age 11 scholar born do
Alice do dau age 7 scholar born do
Matilda do dau age 3 born Harrietsham
Mary N do dau age 1 born do
Robert J Cuckow nephew age 1 born Hollingbourne
The 1881 census shows Alice Butler age 6 living with Jemima Cutbush; Matilda is living with John (junior); I think you'll still need the parish register lookups to prove the relationships. Sorry I can't help with these.
xx Carol.
(Jemima's marriage to William Cutbush is on freeBMD, Dec 1880)