Sorry for the delay but lots more Hudsons than I realised at first. James Hudson (father of Alfrwed) was married twice and it's possible that he and Florence were the only surviving children from that 2nd marriage. There are several online family trees and the owners might be able to get you contacts with Florence's descendants.
Briefly-
James Hudson (d.1893), auctioneer, m.1 Mary Ann Bell (d.1874); m.2 (1876) Martha Ann Cromie (d.1887).
1.
Margaret May Hudson (1864-1944) m. John Cromie- family.
2.
Robert James Hudson (1866-1871).
3.
Minnie Isabella Hudson (1867-1883).
4.
Annie Edith Hudson (1869-1870).
5.
Robert James Hudson (1871-1934) m.(1891) Agnes Cromie (d.1902); m.(1904) Margaret Hollingsworth (1877-1966).
6.
Adelaide Agnes Hudson (1871-1897).
"Administration of the Estate of Adelaide Agnes Hudson late of Rathfriland County Down Spinster who died 29 June 1897 granted at Belfast to Robert James Hudson Auctioneer."
7. Henry John Hudson (1872-aft.1911), printer compositor.
8. Son (1877-1877).
9.
Florence Nightingale Hudson (12 Aug.1878-18 Aug.1956) m. Rev. George Heron (d.1 Aug.1959).
1. James Hudson Heron (c1904-18 Aug.1981)
2. Norah Margaret Heron (c1907-aft.1911).
3. Rev. George Victor Heron (c1910-alive 1963).
10.
Alfred Teenyson Hudson (13 Nov.1879).
https://familysearch.org/pal:/MM9.1.1/FGN2-WM511.
George Frederick John Hudson (1883-1889).
12.
Samuel William Hudson (1885-1886).