Doh! Forgot about Jason. YOu're right... it all falls apart now. Screw it!
It doesn't have to. Maybe there's a two or three month period between Dick leaving and Tim joining. Batman thinks he can rehabilitate Jason Todd but it doesn't work, Joker beats Jason almost to death and Batman fires him for not following orders and being reckless.
Or maybe Batman just does what he did with Stephanie and uses Jason to make Dick jealous and... You know what, there's really no way to write that without it sounding kind of icky.