Generate TTL-level reset pulse from RS-232 level signal
Well first of all get rid of that capacitor C1. Connect the transistor collector directly to the reset of the AVR processor. 

Also make sure that the GND of the AVR subsystem connects through to the GND of the DTR signal setup.

There is no reason to try to limit the reset pulse width with any capacitor here. Just make sure that the DTR goes to its ++V level for as long as you want the AVR reset to be asserted and then return DTR back to GND or the --V level.