As part of an extensive study of the physical properties of active galactic nuclei (AGN) we report high spatial resolution near-IR integral-field spectroscopy of the narrow-line region (NLR) and coronal-line region (CLR) of seven Seyfert galaxies. These measurements elucidate for the first time the two-dimensional spatial distribution and kinematics of the recombination line Br{gamma} and high-ionization lines [Sivi], [Alix] and [Caviii] on scales <300 pc from the AGN. The observations reveal kinematic signatures of rotation and outflow in the NLR and CLR. The spatially resolved kinematics can be modeled as a combination of an outflow bicone and a rotating disk coincident with the molecular gas. High-excitation emission is seen in both components, suggesting it is leaking out of a clumpy torus. While NGC 1068 (Seyfert 2) is viewed nearly edge-on, intermediate-type Seyferts are viewed at intermediate angles, consistent with unified schemes. A correlation between the outflow velocity and the molecular gas mass in r<30 pc indicates that the accumulation of gas around the AGN increases the collimation and velocity of the outflow. The outflow rate is 2-3 orders of magnitude greater than the accretion rate, implying that the outflow is mass-loaded by the surrounding interstellar medium (ISM). In half of the observed AGN the kinetic power of the outflow is of the order of the power required by two-stage feedback models to be thermally coupled to the ISM and match the M-{sigma}* relation. In these objects the radio jet is clearly interacting with the ISM, indicative of a link between jet power and outflow power.