Use of the word "Dutchy" to describe a personality trait
I am of German heritage and raised in the Midwest. My parents and grandparents used the term dutchy to describe a woman who dressed in and old-fashioned, overly conservative, unflattering manner. They didn't use the term specifically to describe a personality trait, but it could apply to a stern, conservative, old-fashioned person.
The Urban Dictionary online has a number of ideas, but I suspect the OED gets closest
Frequency (in current use): Etymology: < Dutch adj., n.1, and adv. + -y suffix1. Dutch-like. 1893 J. H. Ross in King's Business (New Haven, Connecticut) 127 The faces [in Rembrandt's Scripture pictures] are not ideal but Dutchy.
My suspicion is that this was a late-nineteenth/early-twentieth American expression for a person of Dutch, or possibly German descent, perhaps one who didn't speak English entirely fluently.
Did your great, great grandmother have Dutch or German connections?