Does your DAC have an analog input (like all NuPRIME DACs) or is it digital only?
If it has analog ins, just run the L&R RCA outs out of the AVR, into the RCA analog inputs of the DAC, and you don't need the double connection at the amp, which I am not sure is a good idea (but someone who is more tech savvy might answer that)
Then all you do is select the input you wish to use on the DAC. Of course you will need to preset the gain on the DAC, or in the case of the NuPRIME DACs, the inputs have memory, so it will remember what gain setting was used last.
Again, I am not tech savvy enough to know what might be occurring during the switching process you are seeking, but to error on the safe side, I would turn the amp off before switching back and forth. Hopefully it is perfectly harmless.