In those cases it's more likely they just didn't have the resources to respond, espesially for the ottomans. They fall into that same two fronts problem the Byzantines had. If the Ottomans, or in earlier centuries the Byzantines, were fighting in the east, they couldn't wage a war in the west.
The war mechanics in EU4 don't account for loyalty among generals. Giving a huge army to a general is just asking for a coup.
Ofc my knowledge of history focused mainly on the Byzantines earlier and less on this time period. But in the history I know Vassals were a fantastic buffer against invaders that were used because it's very difficult to muster an army against an invader quickly, espesially if said country is already at war.
In this, I think the only change I'd recommend is for one to declare war on the vassal directly and making the mother country an automatic co-beligerant of the war. This is probably better then forcing the war upon the mother country only.