I can find many schematics on how to operate the DC controlled relay to operate the AC load, but what to do if the relay itself is driven/operated by 220 VAC?
Making one more relay for relay? Or make some sort of small SSR to drive relay?
The MOC302X optocouplers are really intended to be used as TRIAC drivers. You won't see much design information on how to use them to directly drive AC loads. Using them to successfully drive an inductive load will be very dependent on the snubber design and will probably require some experimentation to get it right.
If you must use the AC relay, I would use a small SSR to drive the coil.
MOC3023 rated pulsed output current is up to 1A. Safe continous current based on thermal dissipation is about 100 mA.
The rated current of the relay coil is about 5 mA, so the optocoupler I recommend is suitable with a large margin.
I myself quite often use such optocouplers instead of relays to control low-power AC loads.
If you are confused that this is an optocoupler for controlling a triac, then you can take AQH3223 instead, which are declared by the manufacturer exact as relays. The connection will be same.