I'd start by putting the Arduino in control of the SP0256's /Reset (2) and /Sby_Reset (25) pins. Tie the two SP0256 resets together, connect them to an unused Arduino I/O, and in your sketch's setup() function, set that I/O as an output and set it low for 100ms then set it back high. The 100ms is much much longer than the Archer SP0256 datasheet's minimum reset pulse length of 100us because after powerup, you need to be certain the power supply is stable before releasing the SP0256 from reset. If you want to reset it during operation a 1ms low going reset pulse should be sufficient.
Now you've got me inspired to dig out a SP0256 from the box of bits I got when Tandy UK went under and see what I can get out of it.