Why is there a sudden change in current between \$t=0^{-}\$ and \$t=0^{+}\$ when an active inductor is connected in series with a relaxed inductor?
It may help to recognize that this is analogous to connecting capacitors charged to different voltages in parallel.  In the case of inductors it's conservation of flux rather than charge that is at play. So, by inspection, the current just after the switch opens will be 2/3 * I0. 

As with the capacitor dual, you will also find that the energy is (apparently) not conserved because energy is lost in the switch opening. The energy in the inductors before the switch opening is 0.5*2*3^2 = 9J. The energy in the inductors after the switch opens is 0.5*2*2^2 + 0.5* 1* 2^2 = 8J.