Your hand drawing, use of a single 9V battery will not work.
You have two power domains, one 0, 9, the other 0, -9, so need
two batteries wired like this
Now your dac runs fine off + supply, driving LM317. Problem is your
LM337 ref pin is below ground, which DAC cannot produce. So you have
to use an OpAmp level translator run off split supplies.
Use this to create the level translator -
https://masteringelectronicsdesign.com/differential-amplifier-calculator-2/
I am assuming you want the LM337 LM317 circuits to track in V, just opposite polarity ?
Lastly you ignored the design recommendations to get the correct operation between the
DAC and LM317, also LM337, posted in #16, so you wont get the range you are asking for
until you utilize that circuit.
Regards, Dana.