Here's one solution for your problem:
I've made one ahk script that accepts 2 command line parameters: the first program and the second program.
It'll launch the first program, and when that program is closed, it'll launch the second one.
I've included a demo shortcut that demonstrates how to use this program.
So, configure the shortcut properly and just have your client open thunderbird through this it.
(the program is attached to this post, both in source-code and compiled version.)