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.
There is a couple of methods commonly used in your situation.
1) (not recommended) Use the protective Earth ground connection that should be present in your box instead of a Neutral connection.
Note that although this works quite well from a technical perspective, it won't pass UL or CSA certification (nor most other certifying authorities). One reason is that if the Earth connection should become disconnected or broken, you are deliberately passing current down the Earth conductor, which would cause it to become live in the event of a disconnected Earth.
2) Do some fancy phase control during the ON state.
Stealing power while the switch is OFF (open) is easy - you treat the Switched conductor as if it were the Neutral. That is: the load provides the continuity to the Neutral conductor. You will have approximately the full AC mains voltage across the switch.
This is (usually) OK so long as you are stealing only a few mA. However, there are some loads that this won't work with - I'm thinking of the little Egg-shaped strobe lights that used to be in discos in decades past. There may be other loads that aren't happy with this as well.
Stealing power when the switch is ON (closed) is a little more difficult. What you do is use a triac as the switching element and delay turning the triac on until the voltage across the triac is the desired supply voltage that you are trying to achieve. A diode picks that voltage off and stores it in a bulk storage capacitor. Then turn the triac ON.
Modern X10 light switches and some other smart light dimmers work this way.
Best Answer
A relay may be used, instead of a switch, to control a light.
The relay coil is to be kept energised for as long as the light is to remain lit. A standard electromagnetic relay would be designed for continuous duty with respect to its coil and contacts and would not get damaged, provided that its voltage and current ratings are not exceeded and snubbers are used to minimise damage to its contacts while switching inductive loads. Likewise, with capacitive loads, it should be ensured that the contact rating is not exceeded, while high charging currents are being switched, that could result in welding of contacts.
Latching relays may also be used to avoid coil consumption after the switching action has taken place. A latching relay would require only a pulse input to its coil / coils, for it to be set or reset.
Considering its voltage and current ratings, the relay referred to would be good enough to control AC/DC domestic lights.
It would be advisable to take the assistance of competent personnel to carry out the modification.