OP this thread has gone one for so many pages now but I think if you read back in the first couple you will really have your answers.
Yes, it does sound like your neighbour has issues with you and is a bit snooty. However with this issue you are giving her a reason to be and you really don't seem interested in resolving it with her.
In one of your posts on page two you've perhaps explained the entire problem of her snootiness with this: "We have a lovely garden but are not keen gardeners so other than the odd tidy, we are not too worried - but the neighbours now are keen gardeners. When we lived in the new housing estate, most gardens were postage stamp sized and people were not especially garden proud."
I'm not saying that her attitude is right, but she's seen you arrive in your house with the lovely garden, she's a very keen gardener, and you say you have no interest in yours other than a quick tidy round.
If she's judging you on appearence then this is right where I think it started. She cares about and spends time on her garden and she will judge others on the state of thiers (and we all do it about something.)
And now her lovely garden that she has worked long and hard on is being spoilt for her by cats she believes belong to you.
In the same post I just quoted you also said "I do see the logic behind: 'they are your pet so you clean up after them.' I guess I am questioning for a number of reasons, which I realise do not challenge the above logic."
Well, that logic is her logic and that's why she has asked you to clean up in her garden. By refusing to clean up now you are challenging that logic.
But if you really do not want to clean up in her garden then you still should do something.
Even your most vocal supporters on here have admitted that cats wander far and wide and shit while they do it. You can blame the other neighbours cats all you like but yours are going to the toilet somewhere other than your garden and their litter tray. Put aside the issue of ownership for the particular pile of shit in her garden. You own cats that are shitting somewhere and that shit ultimately belongs to you. Because I don't buy this 'caretaker of cats' argument, if someone stole or harmed that cat you'd be saying "my cat!" quicker than it could shit in a newly dug flower bed. You own the cat, you own the shit.
So even though she might be wrong and it's not your cats, or only your cats, that are shitting in her garden, you have to accept that they might be responsible for some of it and they are definately doing it somewhere.
As this particular neighbour has complained, and this issue really is only going to get worse, can you not agree with her some of the other solutions that have been offered to you here?
Buy her the sonic repelling gadget and the smelly sticks that someone linked here. Tell here that if she catches your cats in the act you fully support her squirting them with water.
Be the bigger person, as even your own mother thinks you should be, before you become one of those people you read about in the papers who have had a 20 year running feud with their neighbours over two inches of hedging and a pot plant a cat that will be long dead while the argument and unpleasantness live on.
To do otherwise is to run the risk of all that and have a letter box filled with poo in the middle of the night or your cats harmed, made ill or even killed if the neigbour takes matters into her own hands and resorts to some of the things discussed here (such as the broken glass, chilli pepper or poison).