I've used a cron script (written in PHP, not executed from the webserver) to check a server is up and restart the server.
However, I wouldn't do this from a server-created process, because you know you're about to kill the parent process, which has bad implications for the child.
The simplest method would be to have a file /tmp/RESTART_APACHE which PHP can create, and which the cron script checks for. If the cron script sees the file /tmp/RESTART_APACHE then it does a proper restart of Apache.
Using a cron script will introduce a delay (up to 60s if you run it each minute), but apart from that should work as you want.
Depending on how you intend using this, that may do the trick.
(You probably want to use a different directory than /tmp/ to set permissions and prevent anyone on the server being able to create the file.)
EDIT: Please see Aaron H's comment to this post. I agree with what he says: you really do want to be careful that the ability to restart your webserver is not a service generally available to the public.
Restrict access to the system which can trigger the restart; ensure that the file which triggers the restart has restrictive permissions so only the web process can create that file, and generally be smart.