Ok in the set-up i just mentioned it would be like Mixer channs outputs 1-8 to analog 1-8 input on your digi003, then channels 9-16 on your mixer outputs to the Alesis AI3 analog inputs, then Alesis AI3 Adat output to the ADAT input on your 003, finally, channels 17 & 18 in your mixer output to the DAT input, and the DAT SPDIF output to the digi003. Thats to record
Now outputs of the digi (mixing) Analog 1-8 outputs on the digi to 1-8 inputs on the mixboard, adat output on the digi003 to the adat input on the AI3, analog output on the AI3 to channels 9-16 on the mixboard, finally, Digi003 spdif output to the DAT spdif input, DAT analog ouput to the mixboard chans 17&18
I hope this clears things up a bit