I agree with the above: you should test the 555 timer circuit first to be sure it works on its own.
If the relay is already being driven from a transistor, there's no need for a diode.
Have you connected the 0V rails of both circuits together? There needs to be a common 0V reference for the circuits to interface with one another.
If a pulse is applied to pin 2 for longer than the length of the delay, the output will stay high until the input goes low again. If this is a problem, you should AC couple pin 2 to the trigger signal via a small capacitor (100pF to 100nF) and bias it to +V with a pull-up resistor (10k to 1M).
See the application note linked below for more information:http://www.doctronics.co.uk/pdf_files/555an.pdf