Hi Carol,
It has me stumped too! I have tried to trace Arabella, like you I found the christening but nothing else?
I found this on the 1861 census - thinking it might fit your Matthew and Elizabeth, due to the Lythe connection, here goes:
Matthew Stonehouse, b.1801, Lythe.
Elizabeth, b.1809, Whitby.
Christopher. b.1827, Lythe,
Jane (Hind) b. 1857 Great Broughton/Little Broughton, (grand-daughter)
At the time of the census they all lived in Great Broughton.
Hope this helps.