I had a similar issue a while back when I was switching between 3 characters. Basically the issue is that the movement mode for the Character class is static, so its shared between all characters on the level. So as you switch characters, the new movement mode is propagated to all children of the Character class (see the floating below).
The only "real" fix would be to modify the character class itself. I ended up restricting the switch to when the character is standing (Movement Mode Walking). Does your solution fix the issues on the vid?