How can I get my father to know that I am playing guitar, but not have him hear it?

I don't know why your father “has to know” you're playing guitar but can't you just tell him when you're playing the guitar?

If it's loud enough for him to hear then there's nothing you can do to stop him listening but you could ask him not to comment on it and pretend he didn't hear you.

Got a computer or phone in the practice room (that you're not using for a metronome/tuner)?  Set up a Skype or Zoom to your father's phone and then mute your side.  He can then see you but not hear you.

Or just let him hear.  What's the point of playing guitar if nobody else will ever hear it?

You have to start somewhere with letting people hear you.  If your nervousness is anything like mine is (yes.."is", not "was"), you may never be fully comfortable playing for others.  You can get some control of your nerves, though, and have some fun.  But the nerves and fears might not go away entirely.

They won't go away at all if you don't take action, though.  Once you see that nothing hits the fan when you do let someone listen, the next time gets easier. 

Set yourself a small goal at first.  Mine was, "If they aren't running screaming from the building with blood coming from their ears after I perform, then I've done my job."  Sure, maybe they were running; but if they're not bleeding then mission accomplished.   I can work on running or screaming next week.