Thank you @Paul_B, you're a star.
I'm not sure I understand what do you mean when you say "what will be powering your motors". The motors are electrical, and are connected to the house's power line.
Regarding the total load on each power supply, it's probably not going to be much on one of them, as it will be only powering the ESP, which in turn plugs into the module, but through the VCC pin.
Then the other PSU is the one actually powering the module via the JD-VCC. If the PSU is rated for 600mA and the relays draw 85mA max, it should be able to handle a 6 channel module, right? in worst case scenario it would be drawing 510mA.
About the switches, they are the tipycal house switches (btcino if you need to know) that will be located at the side of the door the shutters are located at. This means there will be about 1,5-2 m cable between them and the micro. Also, what difference does it make having pull-up or pull-down resistors? I already did the previous circuit (the one with the 3 individual relay modules) with pull-down resistors and seems to be working fine. Do I need to change it?