Bad news first: only one process can access the camera at a given time, and raspivid is (for the most part) non-interactive, so I'm afraid you won't be able to use a second raspivid process to control the first one (the second process will attempt to open the camera and find it already locked by the first process).
Now the good news: it's certainly possible to manipulate the brightness and contrast of the camera (and many other things!) while it's running (and recording), so it shouldn't be terribly difficult to create a script which allows such manipulation from the initial SSH session.
Here's a little script which uses curses (a venerable console interface library) to provide a simple keystroke based interface to the camera. It allows adjusting brightness, contrast, saturation while the camera is running, and permits recording to be started and stopped (and being text based obviously runs happily in an SSH session):
#!/usr/bin/env python
import sys
import picamera
import curses
def main(window):
with picamera.PiCamera() as camera:
camera.resolution = (1280, 720)
camera.framerate = 24
camera.start_preview()
while True:
window.addstr(0, 0, 'Press Q to quit')
window.addstr(2, 0, 'Brightness: %5d (W/S)' % camera.brightness)
window.addstr(3, 0, 'Contrast: %5d (E/D)' % camera.contrast)
window.addstr(4, 0, 'Saturation: %5d (R/F)' % camera.saturation)
window.addstr(5, 0, 'Recording: %5s (Space)' % camera.recording)
window.refresh()
c = sys.stdin.read(1).lower()
if c == 'q':
break
elif c == 'w':
camera.brightness = min(camera.brightness + 1, 100)
elif c == 's':
camera.brightness = max(camera.brightness - 1, 0)
elif c == 'e':
camera.contrast = min(camera.contrast + 1, 100)
elif c == 'd':
camera.contrast = max(camera.contrast - 1, -100)
elif c == 'r':
camera.saturation = min(camera.saturation + 1, 100)
elif c == 'f':
camera.saturation = max(camera.saturation - 1, -100)
elif c == ' ':
if camera.recording:
camera.stop_recording()
else:
camera.start_recording('video.h264')
curses.initscr()
curses.wrapper(main)
Obviously you could use some other interface (network or even GPIO based) to talk to the process while it's running, but hopefully that demonstrates the principle!