Hi! This one interests me too as I'm descended from William Wilson (great-great-greatgrandfather).
There are a lot of public family trees on Ancestry which include this couple, but 90% of them have Ann married to Richard. I don't think this can be right (and it probably results from indiscriminate copying)
a) because the children have the mother's surname
b) because Richard had ecstatically married the heiress Anne Puleston only a little over a year before Charles was born - "Richard Parry Price married Anne Puleston of Brynypys, Flint. 23rd October, 1764, at Biddulph, in Staffordshire, by the Rev. John Gresley. In Mr Parry Price's diary, this event is thus recorded: " Made the happiest man in the world by being married to my dearest Nancy at Biddulph" http://stmarysbirkenhead.blogspot.co.uk/2012/05/richard-parr...
c) so far as I can judge, Richard Parry Price and Ann Wilson were of rather different social classes (e.g. William's son George became a groom and coachman in Rochdale)
Of the few public family trees on Ancestry which do state that Ann was Richard's mistress, I picked that of Kara10New as she seemed to have the most detail, even including a nickname 'Lady Jane' for Ann Wilson - sounds like sarcasm on the part of the villagers! I have recently contacted Kara asking how she got this info; she has acknowledged but not given her sources yet.
The only scenario that I can think of (and I stress this is speculative!)is that Richard could have been much distressed if Anne Puleston, his second wife, had died in/after childbirth as did the first (Dorothy Byrne, m.18/11/1758 son born Nov 1761, Dorothy d.11/12/1761). He could well have turned to one of the servants for comfort without commitment.
I'll happily send my family tree in its current state of progress if you want info on William Wilson's descendants, but it's in pdf format (not accepted on this system) so I'll need your email address. Mine is firstname.lastname@example.org