In 1440 John Pykmere was described as 'a diligent intermediary between the king and his people in North Wales' and was pardoned for a recognizance of £200 so he must have been fairly wealthy. Pykmere seems to be a Cheshire place-name so, presumably, John was an English merchant in Caernarfon.
For Joan to be so prominently mentioned and for heirs to be specified it is clear she was of importance. In this context the only reasonable identification is that she was Joan the widow of Gwilym ap Gruffudd.
According to http://www.penrose.org/getperson.php?personID=I40628&tree=penrose
Jonet Stanlet (abt 1380 - 1466)
Jonet is the daughter of William Stanley (abt 1348-bef 1428) and Margery de Hooton (abt 1352-1430). She had 2 brothers, William and John. She had 3 husbands: Robert Paris, Judge (m. abt 1397), Gwilym ap Gryffydd (m. abt 1400) and John Pikine.
Penrose sources are:
S R Meyrick, 1846, Heraldic Visitation of Wales
Vol 2 p. 89 (Footnote 1) online copy
J E Griffith, 1914, Pedigrees of Anglesey & Caernarvonshire Families
pp. 106, 185 -- Griffith-Shows all his children as of the 2nd wife except Tudur Vychan of Penmynydd.
Similar at http://geneagraphie.com/getperson.php?personID=I116287&tree=1
where the name is transcribed as John Pikemere.
Slightly fuller for John Pikemere at http://histfam.familysearch.org/getperson.php?personID=I63918&tree=Welsh
where it appears John and Joan had a daughter, Letis, born abt. 1430
The well-timed submission of Gwilym ap Gruffudd (d. 1431), landholder, during the Glyn D r revolt enabled him to add substantially to his lands at the expense of some of his kinsmen and to become the most powerful figure in the principality of north Wales, where his family, the Griffiths of Penrhyn, were to dominate until 1540. Married, secondly, Joan Stanley, daughter of Sir William Stanley of Hooton (Welsh Biography Online
Biographical source include;