That antenna cable runs from the diversity on the pass. side to the head unit correct? My first recommendation would be to make sure that the cable will fix the issue first before complete disassembly of the interior by plugging in the diversity side then to the back of the radio. If the issue is not resolve, then you know its not the cable. If the issue is resolved, then you'll need to disassemble the drivers side B-pillar and C-pillar. Remove both front and rear sill plates, removal of rear seat bottom and seat back to expose harness. You'll then need to GENTLY cut away the fabric tape to remove the antenna cable then reinstall the new cable. It's not a bad job to perform, but if you're not careful with wire routing you could do more damage then you'll want.
I see that you're located in Woodland. If you feel that the task may be a little more than your husband wants to tackle PM me and I would like to discuss the issue at hand.
On a side note, in the 12+ years at a BMW dealership I have never once replaced an antenna cable except for one that we did for a body shop because it was severed.