As part of an extensive study of the physical properties of active galactic nuclei (AGNs) 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 Brγ and high-ionization lines [Si VI], [Al IX], and [Ca VIII] 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 AGNs, 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 to match the M BH-σ* relation. In these objects, the radio jet is clearly interacting with the ISM, indicative of a link between jet power and outflow power.