So I want to install three antennas on the car. These would all be NMO type quarter wave base loaded whip antennas. The configuration I considered is as follows: The 42MHZ antenna would
be in the center of the roof The six meter whip would be behind it and the 2 meter antenna would be on the trunk. I figured if I'm not using the 77,(which would probably be a good portion
of the time) I can AB switch the six and two meter antennas into the Yaesu.

You might want to consider placing the 2-meter antenna on the roof.
If it's on the trunk, it will be trying to "look through" the car
cabin when radiating in the forward direction, and you may find that
signal propagation in that direction isn't good at low angles.

Your low-band antenna would probably be somewhat less affected by this
(being for a longer-wavelength frequency, and probably physically
longer as well).