I suggest you join the Sussex Family History Group as they have a lot of online records for members and it is not expensive. They have numerous Spilsted/Spilstead entries listed. Stephen and Ann seem to have had at least eight children, though some died as infants.
I wonder if Jemima's second name was Ellen? There is another child named Jemima Ellen baptised in 1862, daughter of Alfred who may well be your Jemima's brother.