Dear Polly ~
There is a helpful discussion of the Ardern-Arden family published in French, Shakspeareana Genealogica Pt. 2 (1869): 445. I've copied the pertinent part of the discussion below.
The full discussion may be viewed at the following weblink:
https://books.google.com/books?id=efE8AAAAcAAJ&pg=PA445
There is also Arden pedigree chart on page 441.
As you can see, the author Mr. French supplies additional details on the Ardern-Arches descent, including the name of Joan Ardern's mother, Joan Trillow, and paternal grandmother, Margaret Molineux.
Mr. French appears to quote from "Visit. Harl. 1167." That's probably a visitation which is print and which can be consulted by you.
Curiously Mr. French refers to Joan Ardern's husband as Richard Archer, whereas his name was clearly Arches. He specifically states that Joan Ardern and Richard Archer are the parents of Joan, wife of Sir John Dynham. So he concurs with Roskell's and VCH Oxford's account of this family.
Mr. French states that Joan (Ardern) Arches' great-grandparents were Sir Robert Ardern and his wife, Nichole Bardolf. Nichole Bardolf's royal ancestry is traced in my book, Royal Ancestry (5 volume set), published in 2013. Contact me offlist about ordering a copy of the Royal Ancestry book.
I might add that if Mr. French has the earlier pedigree of the Ardern family correctly stated, then Joan (Ardern) Arches would also have a long meandering descent from the Pinkney, Lucy, and Basset families which I worked out last year.
I can't vouch for the accuracy of all of Mr. French's statements. I can say that he was a better than average genealogist but not without error. So, as with all secondary sources, you need to verify everything Mr. French says against contemporary records.
Best always, Douglas Richardson, Salt Lake City, Utah
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Reference: French, Shakspeareana Genealogica Pt. 2 (1869): 445
"Sir Robert de Arden of Drayton, Knight, who by his wife Nicola, daughter and heir of _____ Bardolf, had, with a daughter, Nicola, married to Richard, son of Sir Ralph Basset, Kt., a son, Sir Giles de Arden, Knight, whose wife was Margaret, daughter of Sir John Molineux, Knight, and their son, Giles de Arden, (obt. vit. pat.), by his wife, Johanna, daughter of Sir John Trillow, Knight, had two daughters, his co-heirs, of whom the second, Johanna, married Sir Richard Archer, Knight, and the eldest, Margaret, married Ludovick Grevill, and their son William Grevill is the ancestor of the Warwickshire family of that name, who became Lords Brooks, and Earls of Warwick, and who quartered the arms of Arden in consequence of their descent from Sir Robert, or Lord Arden, as will be seen hereafter. Sir Richard Archer and his wife Johanna Arden had a daughter Johanna, who married Sir John Dinham, Knight. 'The Inquisition taken at Oxford after the death of Sir Giles Arden, Knight, 5 Ric. II., declares that Margaret and Johanna, daughters of Giles Arden, son of the said Sir Giles Arden, Knight, are heirs of the said Sir Giles Arden, Knight,' Visit. Harl. 1167. Sir John Dinham's second daughter Joan (by his wife Joan Archer) married John, eighth Lord Zouche of Harringworth ...." END OF QUOTE.