The girl tended to want to monopolize her father's affection and view her mother as a rival.

Literal

Girl [subject-が] father's affection [object-を] monopolize want [quotative-と] think, mother [object-を] rival [quotative-と] view tended.

A psychology-flavored sentence evoking the Electra complex. 独占したい (want to monopolize) uses ~たい; ~がちであった means 'tended to.' みなす means 'to regard as, to consider.'