Couple things:
-You cannot actually SDI throws (I think there are 2, maybe 3 exceptions in the game) as a general rule
-You can chainthrow in fox dittos on reaction to the opponent's DI, its guaranteed (unless there are platforms)
-The best way to mess them up is to try to neutral DI then after you fly straight up, make slight adjustments to your trajectory forcing him to dash dance/pivot grab/uptilt. While doing this you can shake the control stick to escape the tumbling animation at the fastest possible moment and either mash jump or try to shine out of it.
-Alternatively you can DI off stage for the chainthrow to end, but that is only of debatable effectiveness; it depends how confident you are in being able to recover after getting sent off stage, versus taking the guaranteed damage/hoping they mess up.