Let's try and sort out facts.
Robert Woods b in preston? 1912 parents William (SURNAME= WOODS)? and Alice Marchbank. (the paternal grandparents)
William (SURNAME= Woods) ?b ? (where)? parents Robert Woods and Sarah Jane Gregson (m 1888)
Great Grandma MILLER lived in Malt St, Preston. (OKAY. WHEN)
If Miller is a Great-grandma then either :
she is the parent of Alice Marchbanks, or
she's on the maternal line which you haven't even mentioned.
PAuline