I am new to the concept of two wheeled vehicles, so I started with a Kawasaki H2.....

Starting with your client, how do you know your kill()s are working? If the mysterious check_arguments() returned garbage, how would you know? Does the mysterious init_signal() actually work? How do you know?

Also, in your server, how do you know your kill()s are working?

Those are implementation basics; and you need to cross them out.

Next is, are you working on a flawed concept?

You are relying on signal queuing maintaining time order, which is an assumption worth examination. I think it is fair game for signals to be prioritized by identity; so if there are 4 queued signals for SIGUSR1 and 5 for SIGUSR2, the order you might observe them could be: 1,1,1,1,2,2,2,2,2 or 1,2,1,2,1,2,1,2,2 or 1,1,2,2,1,1,2,2,2

Even if you work out the strategy used by your particular implementation (linux a.b.c.d) might change it on a whim.

The H2 is a notoriously difficult bike to ride; yet was quite popular.

Asynchronous communication is notoriously difficult. Understanding why is an important exercise.