Are Campanula and Caesalpinia part of the same family?
no
Campanula
Campanula is one of several genera in the family Campanulaceae with the common name bellflower.
 It takes both its common and its scientific name from its bell-shaped flowers—"campanula" is Latin for "little bell".
Caesalpinia
Caesalpinia is a genus of flowering plants in the legume family, Fabaceae.
 Historically, membership within the genus has been highly variable, with different publications including anywhere from 70 to 165 species, depending largely on the inclusion or exclusion of species alternately listed under genera such as "Hoffmannseggia".
 It contains tropical or subtropical woody plants.
 The generic name honors the botanist, physician, and philosopher Andrea Cesalpino (1519–1603).
Campanula uniflora
Campanula uniflora, known commonly as arctic bellflower and arctic harebell, is a short and slender rhizomatous perennial in the bellflower family Campanulaceae.
 It is distributed in arctic North America, including the Rocky Mountains and Greenland, in the Asian part of Beringia and in Iceland, Svalbard, the Scandes Mountains and Novaja Zemlja.