The PiCapture HD1 will attempt to deliver the video stream at the same frame rate that it receives. There are some limitations in the ability of the Raspberry Pi to handle the encoding of 60fps video, and so there would be some dropped frames at that rate. Other than that, the frame rate is determined by the source.
There is a “frame skip” option for the HD1, which causes exactly 1/2 of the received frames to be sent over the camera interface to the GPU. This means that if there is a 60fps video source there would be 30fps delivered to the Raspberry Pi. If you can set your source to 60fps you might be able to achieve what you want that way.
I don’t know if v4l2 provides control over the frame rate, and would suggest asking the v4l2 community about this. We have used v4l2 with PiCapture successfully.