Newly developed methods to perform brain PET scans of freely moving animals require to perform rigid motion correction reconstruction. In these images, in addition to the loss of spatial resolution due to the spatially variant resolution of the scanner, the spatial resolution is motion dependent since the animal can be located anywhere inside the scanner FOV during the scan. Here, we developed a method to calculate the spatially variant and motion dependent blurring kernels (SV-PSF-MC) in the image space to be used for the resolution modelling in motion correction reconstruction. After estimating and parametrizing the spatially variant resolution of the PET scanner, motion dependent blurring kernels are calculated as the superposition of the point spread function of every voxel the object traverse in the image space during the scan under motion. A phantom with capillaries distributed along the radial direction was scanned to verify the efficacy of the resolution modeling using the estimated spatially variant resolution of the scanner. Additionally, a moving resolution phantom experiment was performed to evaluate the use of the SV-PSF-MC kernels. Compared to the use of spatially invariant Gaussian kernel, reconstruction of the capillaries using the estimated spatially variant kernels present more uniform intensity along the radial direction, with a maximum intensity decrease to 45% and 75% using the Gaussian and the spatially variant kernel respectively. The spatial resolution and noise of the motion corrected reconstruction of the resolution phantom was improved using the SV-PSF-MC kernel compared to the Gaussian kernel. The maximum intensity increases about 12% and 25% for the 2.4 and 3.2 mm rods respectively using the SV-PSF-MC kernel compared to the Gaussian kernel. The current method improves the spatial resolution and noise in motion corrected reconstructions used in scans of freely moving animals, allowing improved quantification.