So technically speaking, pushing updates from Active Directory group policies don't exist. The group policy has an interval which can be set low which allows computers to refresh / update its policies but this can cause potential problems of network congestion and high load on your active directory server. The good news is that there's another trick which works but with more eficiency.
The solution is using a third party application called SysInternals Suite (I believe it is now owned by MS)
You can download it from http://www.systeminternals.com
Extract it into a directory such as C:\sysinternals
Now you'll need to get to a command prompt (HINT: Run -> cmd.exe)
In the command prompt type each line and press enter as follows:
PsExec.exe \\COMPUTER1 gpupdate /force
The above command essentially tells the remote computer "COMPUTER1" to execute gpupdate /force
gpupdate /force basically makes the computer refresh its group policy by pulling it from the active directory
If you are successful, you'll see a response like
User Policy update has completed successfully.
Computer Policy update has completed successfully.
gpupdate exited on COMPUTER1 with error code 0.
With a little scripting, you'd be able to do this command on multiple computers