I wouldn't have waited until we got home. I would have calmly said, "Excuse me, that was uncalled for. Can we try this again from the top? Only this time, without the embellishments?"
Or you could say, "Where on earth did that come from? Now let's try this again..." etc.
When something like this happens in front of bystanders, it's not good for either of you. Plus there is always the importance of dealing with it immediately, if it's possible (considering TEC methods and baskets, etc).
There is also the very interesting factor of bad behaviour for the benefit of a young bystander - even PCs do this, it's typical teen behaviour which in a difficult child can get really out of hand. When easy child began to be disrespectful in front of her friends, I was shocked - she was a good kid who was polite and well-behaved as a rule. The first time, I waited until later to talk to her and said, "Why did you do this? I was embarrassed for you and I could see that you embarrassed your friends, too, by being so disrespectful to me in front of them." She was upset and angry with herself, didn't know why she had done it.
The next time I called her on it in front of her friends. I wasn't going to have a blazing row with her in front of them, but I did remind her of our earlier conversation. And again afterwards, we talked and agreed to set up a code so I could warn her to back off.
I don't require subservience form my kids but I do require respect, especially in public. In return, I show them respect.
A good guide to your parental response especially when they reach their teens - I treat them as I would a visitor to my home, perhaps a tenant, who has suddenly begun to behave inappropriately. We forgive a lot, we might comment but not too harshly, but still say what we feel we need to say to defend our honour in our own place.
With banning him from going to his church group - the possibility of this was not in his mind when he spoke disrespectfully. It came on him out of the blue, which is why he was so angry with you about it. Basically, it wasn't on the table at all, until you said, "It's not happening." In his mind, this was unfair. As a result, instead of focussing (as he should have) on why you banned attending the church group, he was instead focussed on the injustice of your behaviour to him, so I suspect nothing got learnt.
I would suggest an alternative (in the event of future recurrences) - ask him what he feels a suitable punishment would be. Also ask him if he feels that taking that foul mouth of his to church is really such a good idea. This helps him better see the connection between his transgressions and the punishment you want imposed. It also gives him an opportunity to apologise.
If you can do this as soon as possible (without escalating his temper) then your response will have the most beneficial outcome possible for him.
It also needs to be done each time, over and over, with you keeping your cool even when he loses his.
It's a pain, it's a hassle, but it does ease with time and persistence. It also is teaching him each time that although you're not going to shout back at him, you're also not going to accept being treated with disrespect.
Did you ever find out what it was he mumbled? Was it intended as a confidential aside to you (such as, "I'm fed up with my friend today, he's being a jerk and I want to go home so we can send him home") or was it something you weren't supposed to hear (such as, "It is such a drag having to be chaperoned by my mother at the pool; and the girl I wanted to see isn't here anyway, this is a waste of time today.")? If either of these, by asking him to repeat himself louder, it could have been causing embarrassment. Not that this is a valid excuse, only it helps to understand what the trigger was so you can avoid it in the future (perhaps by advising him to not say anything likely to be embarrassing, under such circumstances, in future).
Marg