Any obvious problems with this DIY home automation?
Obvious problems: Well yes. As drawn right now, there is some confusion but:

1: Either you don't get 220V to your secondary relay (The one connected to the Arduino) because the line leaving your primary relay going left is a trigger signal line, rather than a power line OR

2: You DO get 220V to your secondary relay and you cannot trigger your first relay because the line leaving your primary relay going left is a power line, rather than a trigger signal line.

My first recommendation would be to redraw your diagram with clear labels on all wires.