HI Les, yes I did spell Princes correctly! and Risborough too i hope

there were two Ada Williams b. 1870 one belonging to Reuben & Edith and the other to John & Ann (your one)
the Ada who doth belong ot Reuben & Edith is with them again in 1891.
but your Ada could quite possibly have been married by 1891 as she would have been 21 then [in 1891]
I thought that maybe the children had been intutionalised and put down by their initials mand maybe born Bucks. but again no positive matches.
if they were with other family members particularly their mothers they could quite easily have been put under that surname as opposed to Williams
there is a Kate Whiting adopted child in Hastings b circa 1877 but i wondered if she had taken on the Whiting name but it appears Whiting was her birth name as the family she is with have a different surname.
hold on will try to find her again
re William Jnr, did his parents die before him? this would explain the 'missing' info from the CWGC site.
where was William Jnr born and what did the birth cert give for his mothers name?