John, Constable of Chester, Baron of Halton - John de Lacy's daughter Joan of Chester who married Peter I de Brus

Hello -
So there seems to be a small hiccup between John and his daughter Joan who married Peter I de Brus. In Douglas Richardson, Royal Ancestry, Vol. p. 214, III, p. 464 vi, and Vol. V p. 156 he lists Joan as a daughter.
This Joan on Geni is marked as the wife of Peter I de Brus: Joan de Grammaire
She is a Joan, but not Joan of Chester de Lacy.

This is the Peter I de Brus married to the wrong Joan:
Peter de Brus

On that Peter's page it lists his son Peter who married Joan Unknown:
https://fmg.ac/Projects/MedLands/SCOTLAND.htm#AdamBrusdied1143

Our Royal Titled Noble and Commoner Ancestors (who use Richardson as a source) list Joanna de Lacy as Peter I de Brus's wife:
https://our-royal-titled-noble-and-commoner-ancestors.com/p433.htm#...

Wiki Tree lists 2 marriages for Peter I de Brus (although Joan of Chester de Lacy appears to still be alive when Peter passed)
https://www.wikitree.com/wiki/Bruce-2207

So, most of the information shows that Peter I de Brus married Joan of Chester de Lacy and perhaps Joan de Grammarie.
Is there any way to at least ADD Joan of Chester de Lacy to Peter I de Brus as a wife to Peter and a daughter to John de Lacy and Alice FitzRoger de Clavering??
Thank you,
Mary