When Livereload is too much and cmd-tab’ing too little, there’s always this AppleScript.

#!/bin/sh
osascript -e 'tell application "Safari"
  set _url to URL of current tab of front window
  set URL of current tab of front window to _url
end tell'

Put it in your PATH, chmod it +x, and map it to what you like in vim:

map ,r :call system("update_safari.sh")

You could even auto-run it when you save the current buffer:

autocmd BufWritePost <buffer> :call system("update_safari.sh")

Replace <buffer> with * to do it in every buffer.