One-neutron knockout reactions have been performed on a beam of radioactive ^{53}Co in a high-spin isomeric state. The analysis is shown to yield a highly selective population of high-spin states in an exotic nucleus with a significant cross section, and hence represents a technique that is applicable to the planned new generation of fragmentation-based radioactive beam facilities. Additionally, the relative cross sections among the excited states can be predicted to a high level of accuracy when reliable shell-model input is available. The work has resulted in a new level scheme, up to the 11^{+} band-termination state, of the proton-rich nucleus ^{52}Co (Z=27, N=25). This has in turn enabled a study of mirror energy differences in the A=52 odd-odd mirror nuclei, interpreted in terms of isospin-nonconserving (INC) forces in nuclei. The analysis demonstrates the importance of using a full set of J-dependent INC terms to explain the experimental observations.