It sounds like you want the output to be activated when the remote button is pressed, stay activated when the button is released, and be de-activated when the button is pressed again.
Correct?
If so, then your circuit will not work. the output of the remote is a digital bit pattern modulated on the IR light. The output of the 1738 is a recreation of the input digital pattern. T1, C2, and R1 act as an AM detector, to turn the demodulated data burst into an envelope waveform that acts as a single clock pulse for the 4017. A possible problem is that the filter values for C2 and R1 are not correct for the pulse, and ripple in the output waveform is being seen as multiple clock edges.
BUT with no component values, it is impossible to say.
Also, the 4017 outputs cannot source much current. Depending on the values of R2 and R4, the LEDs might be overloading the output stages.
ak