AirPlay connection not available when Apple TV is connected to router with Ethernet cable? Anyone have the same experience?

No, mine works fine.

Make sure that the network created by ethernet is not a different network to the one used for wifi.

Hi. Some older routers don't route the necessary packets between the wired and wireless VLANs. You may be able to enable it in the router settings. Look for multicast routing. For example, my dlink DSL-2750B supplied by Verizon had this problem and no way of fixing it.