Just to clarify. If the ship modul unit only acts access point. You have to put the apple airport express into client mode. It then only bridges its two Ethernet ports
onto the network.
It's will advertise its airplay services as a client through the ship modul wifi. However apple warn that this comes close to the performance limits of the express and dropout can be expected
If the OP has not used client mode then that explains why he can't connect properly.
If he has selected client mode then he will not be able to access the native apple airport wifi , its in effect been turned off, the wifi is being provided by the ship module unit. Connect to its wifi instead ( and then reach the airport express )
If the ship modul is a wifi access point only profile , then it should provide dhcp server services. I don't think airport express does so on client mode
If it doesn't its static ip setup all the way ( which is a pain )
Really the problem is the poor implementation on the ShipModul wifi. It should be capable of acting as a client to an existing wifi AP and be setup via dhcp