Paul, the RAC or any other for that matter is a RECOVERY service, not a vehicle transport service.
Sorry but they are correct to refuse to attend you once you vehicle is at your home, unless you have home start even if it did break down a mile away. you'll probably find in the policy something like " they'll only attend if more than ½ mile from you home" .
Even if you have home start, they're still not a vehicle transprt company, there you take your vehicle from your home to some garage where-ever.
As for the RAC-v-AA debate, I know who's the better of the two, I deal with all of them on a daily basis.
For info I was with the RAC for over 27 years, but left them because they couldn't give me the cover that I wanted for a reasonable price.
There is however no excuse for the RAC operator swearing at you, even so, from the tone of your post I'll bet you did a bit of swearing yourself. If this was the case, the operator should have told you that the call would be terminated if you continued. I'm not saying that you did swear, but in my experience you normally get like for like.