No, you are not doing anything wrong. We need to fly for JER (no surprise!) and invariably have to call BAH to get a Flight+Hotel or +Car organised … connecting flights from the Regions don’t compute!
Just jumped through those hoops on Friday, doing JER-LGW-KIN. Everything on-line failed to recognise the BA now does a daily LGW-JER: instead it kept trying to do JER-LHR-MIA-KIN!!
Having all your options pre-planned before phoning is usually a good idea, of course. Good luck