I use Vimium for Chrome, which allows me to refresh with the r key. When I am using the dev tools I lose focus of the page, and have to click in the page in or
I got pretty frustrated with this too, but my problem is a bit different though. I have dev tools detached (in a separate window) and I always need to click to get back to the page.
I wrote a small applescript that works for me:
tell application "Google Chrome"
activate second window -- if I have dev tools open "second window" is the page
tell second window to tell active tab
set the URL to "Javascript:window.focus();"
end tell
end tell
I have it bound to a shortcut using Spark.
So whenever I'm in a detached dev tools window, I hit my shortcut and focus is put back to the page and I can use Vimium again.