I don't know of any general way to tell whether a process is hung or working. If a process hangs due to a locking issue, then it might consume 0% CPU and you might be able to guess that it is hung and not working; but if it hangs with an infinite loop, the process might make the CPU 100% busy but not accomplish any useful work. And you might have a process communicating on the network, talking to a really slow host with long timeouts; that would not be hung but would consume 0% CPU while waiting.
I think that, in general, the only hope you have is to set up some sort of "watchdog" system, where your sub-process uses inter-process communication to periodically send a signal that means "I'm still alive".
If you can't modify the program you are running as a sub-process, then at least try to figure out why it hangs, and see if you can then figure out a way to guess that it has hung. Maybe it normally has a balanced mix of CPU and I/O, but when it hangs it goes in a tight infinite loop and the CPU usage goes to 100%; that would be your clue that it is time to kill it and restart. Or, maybe it writes to a log file every 30 seconds, and you can monitor the size of the file and restart it if the file doesn't grow. Or, maybe you can put the program in a "verbose" mode where it prints messages as it works (either to stdout or stderr) and you can watch those. Or, if the program works as a daemon, maybe you can actively query it and see if it is alive; for example, if it is a database, send a simple query and see if it succeeds.
So I can't give you a general answer, but I have some hope that you should be able to figure out a way to detect when your specific program hangs.
Finally, the best possible solution would be to figure out why it hangs, and fix the problem so it doesn't happen anymore. This may not be possible, but at least keep it in mind. You don't need to detect the program hanging if the program never hangs anymore!
P.S. I suggest you do a Google search for "how to monitor a process" and see if you get any useful ideas from that.