Two Circuits Running Off of Same Battery Array?

place a 47 ohms in series with each between supply and load. Connect a 10uF across load. In this way you might be able to reduce their interactions. This is basic decoupling. Or you can feed one through a schottkey diode, and place a 10uF across it(between 12-0.6V supply and 12V negative.These capacitors should be very near the load, that is the circuit that takes the current.