i assume
I would not assume here.
what would by my best way to take the tone signal output from the arduino, and convert it into a double inverted pulse signal,
or can i do that via the arduino it's self with code?
What's best is highly subjective.
What you are asking for is called level shifting. There are many ways to do that. The simplest consists of pnp + some resistors that pull the output to -12v.
Your arduino cannot generate a negative signal directly.