She's thinking of leaving again 3

[Sotto]

I think the only time to get involved is if it directly affects you. If 'shared ownership' means S (you) would sometimes have the dog (and you don't want a dog) you can make your decision known.

I would agree that she is trying to make herself more attractive to S by having a dog. She doesn't realise that for the R to improve, she would need to repair at a deeper level. She's looking for an external addition (dog) to try and fix things.

I'm sure your S can see the situation for what it is. If your S asks for your view - you can always tell him 'I guess it's up to your Mum if she wants to get a dog.'

Hope this helps a little