Typically you want to completely isolate the AC voltage from the rest of the circuit. This is a safety issue, and it's done to make sure no harmful AC voltage leaks into the DC circuits. Most people would even recommend isolating the neutral line because there could be harmful current on that wire as well. This is usually done with a transformer. The delta-connected AC will go into a transformer. The output of the transformer goes into the rest of the supply circuit or whatever it is. You said this was a power supply, so this will most likely be a step-down transformer.
The DC lines should be isolated as well, depending on the use-case. If you are running DC power to many different devices, or chaining supplies together (which you mentioned), you will want to isolate the DC outputs to avoid ground current loops. Chaining boards together introduces the possibility of different ground references. When two ground levels have different voltages, a current will flow. This can cause noise in your DC circuits. Over short distances, this effect is minimized. You need to decide if you need to isolate DC outputs. Usually this is done using a transformer with multiple taps, which gives you multiple isolated AC outputs, which are fed into separate power supply circuits. If you don't care about noise or ground currents, you don't need to isolate the DC outputs.
To answer your original question, I would not connect the shields together. Typically with power supply circuits you want to completely isolate AC power sources for safety reasons, and isolate DC power sources for noise reasons.