If you had such information for at least two different times, that could be combined to determine the yaw and yaw rate. The "point on the other vehicle" information would need to be the same point on the vehicle for both times. (With such information about only one time, the best you could do is make a "guess" such as "not moving" or "same yaw and yaw rate as me".)
You would need to use the information about your own vehicle to convert the information about the other vehicle from relative to absolute coordinates. The change in the other vehicle's position would give you the yaw. The change in the point on the other vehicle, relative to the center of the other vehicle, would represent motion in a circle around that center: the yaw rate.
BTW, since you are interested in determining yaw and yaw rate based on measurements of position, you may find this project useful as an example. I used radar and lidar measurements to estimate the position, yaw, and yaw rate of a vehicle. By combining multiple measurements, it was possible to estimate position more precisely than any of the individual measurements and to estimate yaw and yaw rate which were never directly measured.