Here's a long article (Australian) about Motorhome Inverters...
http://www.rpc.com.au/products/inverters/motorhome-install/Installing-an-Inverter.html
It does not give a specific answer to your problem but does hint at it towards the end where it suggests that owners check that the Inverter they intend to buy will work properly with an RCD. This suggests that some inverters are not suitable to be used with RCDs. My guess is that you have one of those inverters...
Peccavi, May 2009