Hi
I'm not sure how much help this is as it is quite a bit later than your dates, but does appear to relate to Joseph Jr.
Reading and Wokingham have a number of Sedunary's, there is also a Florence, b. Berks. living OOC.
Source, Family Search:
1901, Elington, Hunts. Florence A Sedunary aged 30y, birthplace Wokingham, described as an adopted daughter.
1911, Great Gaddesden, Herts. Florence A Sedunary aged 39y, birthplace Woodley.
She is also found on the Free BMD:
Q2 1871 Florence Adelaide Sedunary, Wokingham. 2c, 374.
There are 2 other Sedunary's in 1873 and 1874.
She married in 1916 to Egbert James Phillips. Her father was a Samuel Sedunari. If she was adopted, she must have retained her birth name.
I have found a Joseph and Ann Sedunary in 1851 in Reading, but I presume that is Joseph Jr and that you have those details. They have a son, Samuel aged 20 and I'm wondering if this is Florence's father (or even grandfather).
A bit of a long shot, and I may be wrong, but I believe Italian women often use/used their maiden names, even after marriage, could this have applied to Ann?
Hope you can get some clues from this.
Regards
Geoff