A number > 0 of 555 timer tutorials warn against holding the trigger of a 555 timer in monostable configuration low for longer than the duration of the output pulse. Why not?
Electronic – What’s wrong with giving a really long low pulse to a 555 timer
555
Related Solutions
If I'm understanding correctly (I have to answer, can't "comment" yet), I think what you're looking for would be an RC trigger for your V2 push button, which can also be used as a solution to get rid of switch contact bounce.
Here is an in-depth video describing how to set-up contact debouncing, which again, I think is what you're after, rather than triggering the reset as you have on V3.
And here is a calculator for helping to determine how long of a pulse you may need for V2. http://www.ladyada.net/library/rccalc.html
Hope this is what you're after.
You just need to use the output of the 555 to drive the base (through a resistor) of an open-collector NPN transistor. Something like this:
simulate this circuit – Schematic created using CircuitLab
In this case, I've chosen R1 to drive about 1 mA into Q1's base, assuming a Vcc of 5 V, and the need to sink less than about 50 mA. If your values are different, adjust accordingly.
Best Answer
As I understand it, the output simply will not go high until the trigger goes high. If the timer times out before the trigger goes high, you will no longer have a uniform pulse-width.
This datasheet has a good description of the behavior: http://www.datasheetarchive.com/pdf-datasheets/Datasheets-25/DSA-494116.html