Sorry, the 59 was typing error. The official Records Office index for the death is
Deaths March quarter of 1924 Kearns Emily Age 49 GRO Ref no Rye 2b 4
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I agree the Mills children's deaths are very much an outside possibility. If the infant who died was born with the Kearns surname, you would need to know Emily's location soon after her marriage in Postsmouth. I got the impression from the 1901 census that she returned to Sussex soon after, and the indexes showed there were no Kearns infants who died in Sussex during those years after her marriage.
If she had a child before she wed, perhaps there is someone who can check the parish baptismal registers for Iden, Playden or Rye c1893 to see if either have an entry that could tie George Alfred (burried Rye aged 21 days) or James Harry Mills to her.
You are unlikely to find any direct descendents from Emily for her only child died, and there is no evidence of her having a furher child in her widowhood, so the line ends there. You may however, be lucky and find someone who traces their line back to one of her seven siblings and their parents who lived in Hoad Mill. Try Genes Reunited for there are two on there that appear to have family ties with Emily's elder brother George born Iden c1859 and another to her younger brother Herbert born Playden 1879. Roy G