One-shot Monostable 555 with long trigger
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.

https://youtu.be/Nj-Q8FQxHhU

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.