Take for example an aeroplane flying at 60 knots IAS with a 60 knot tailwind. Fairly obviously, it will have a groundspeed of 120 knots, and so 120 knots worth of momentum. If that same aeroplane turns into wind, with sufficient added power to compensate for the extra induced drag, then, assuming a relatively instantaneous turn, it would suddenly find itself with 120 knots groundspeed into a 60 knot headwind, resulting in 180 knots airspeed.
That simply isn't true. You can measure inertia with respect to whichever frame of reference you wish to choose. The result is the same. The aeroplane cannot instantaneously change its momentum with respect to either the ground or the air mass.
In your example, for a hypothetical
instantaneous turn the airplane would, as you say, initially continue to have 120 kts groundspeed. However, the point I think you may be missing is that it will initially maintain its same path across the ground, in other words it will also maintain its 60 kts with respect to the air mass, but it will now be pointed in the opposite direction, thus flying backwards and having a negative airspeed of 60 kts, not the positive airspeed of 180 kts you claim. Of course in the real world (everyone knows Harriers and helicopters are Alice in Wonderland!), we turn anything but instantaneously!