That's the bit you can't do!

If the 2 phones are in parallel with each other, then they must also be "in parallel" with the exchange line.
If you want one phone to ring the other, then you must have some way to isolate that ring from the exchange line - and that's called a PABX! (maybe only a very simple one, but still a PABX).

And if you pick up the "dumb" phone, how else can you decide whether that should "call" the "modified" phone or the exchange line?

You've gotta have something somewhere with the (basic) PABX functionality - build it into your "modified" phone if you want, but you still need it and you can not just connect them in parallel on the exchange line.

BEWARE: in many territories it is ILLEGAL to connect non-approved equipment to the Public phone system.
Even if it's not illegal, your phone company will get very cross if you start blowing up their exchange equipment by sending ringing signals "backwards" up the line! :-0