The main issue here is that the parent in question has not got a 'diagnosis' as such although has mentioned in the past that she thinks she has borderline personality disorder. So they're not young carers or anything like that. Their dm is on medication and has a history of various depression-related episodes, but I don't think she communicates about this to the children (11 and 13) so they don't articulate it as anything to do with mental health as such, although the younger one did recently say he thought 'mum has gone a bit mad'. They are increasingly noticing erratic and worrying behaviour towards others and towards them and it is affecting their relationship with her quite seriously which is awful, but they can't really do anything about it and their dad needs to have a sensitive but honest conversation with them as they need extra help understanding her. They have said that they can't talk to her about her behaviour because they are scared of her reaction 
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I'm wondering if anyone has come across a 'if you think your parent has mental health issues' kind of thing on any websites aimed specifically at children? I have had a bit of a look but have not alighted on anything that quite fits. I am not directly involved enough (I am their dad's dp, we don't live together) to be instrumental in anything to do with her treatment or their relationship with her but am just seeking out resources/tools to pass on that might help him with talking to them about it, if I can.