CI HT12E enable control to reduce power consumption
After tweaking with it a little bit, I figured out that that the TE
  pin should be grounded a little longer then the AD pin...  


If the delay is in a few micro seconds or milli Seconds:. 


Add a series resistor between the switch and the TE Pin.
A capacitor between TE pin to ground.
This will also increase ON (high to low) time of the signal. If this is not okay, Addng a diode will help to bypass the RC time constant. 


Let me know the delay you are looking for and I could propose a circuit.