It is confusing that the adaptor that you have purchased works OK with a trailer and not with your caravan. There may be a problem with the caravan wiring. There is no reason why our 13 pin to 7pin adaptor should not work with both a trailer and caravan.
13 pin plug, our ref 128362 is available ex stock complete with wiring diagram. The adaptor to convert to a 7 pin socket on a towing vehicle is our part 131281. I hope this helps.