First of all: That's no PAT. PAT stands for PortAddress Translation. In your case the port remains as it is and thus doesn't get translated at all. If you would forward external tcp 2222 to internal tcp 22, that would be PAT. However, it's just a name..
How did you test your setup? Did you test the DNAT from eth0 (I guess that's your WAN) or did you test it from eth1+? To test DNAT it's recommended to do a real life test. That includes testing from a seperate WAN connection. Did you test ssh with a ssh client or with a port "tester"? Did you check the target device at 192.168.111.2? Be sure to open the devices firewall to allow incoming connections on tcp 22 from public IP addresses.
You might want to test the DNAT by making a tcpdump on the ssh-device to see if there are packets incoming. If so, the ER works as intended and it's probably the ssh-server not responding to the incoming connection.