How do I cope when my Mum and my Sister both talk to me about each other?

Just listen to both and try to make things nicer between them. This will make the situation better in home.

Don't let them use you to let off steam, unless you really don't mind it. Tell them clearly to stop talking behind the other persons back, or tell them that you'll only listen if the other person in actually in the room too. Why can't they just talk to each other, ask them that, that's what I would do.

If you haven't already, you should sit them down together so that they can talk to each other. The way you cope with it is to care about each of them and listen.

I personally go through this same thing with my mother and sister, they are always at each other's throats. Sometimes you have to remember that no matter their issues those issues will never be your burdens even if they go to you about them. Their faults with each other are only theirs. It'd be good to practice meditation/mindfulness and the releasing of any negativity or heaviness you feel is being bestowed upon you.

Tell them to talk to each other instead. Then maybe they will be able to sort out their differences.

Something I found to work when I was faced with this situation was to let them both know where you stand in their relationship. Sometimes it is better to be neutral and not talk to either one about the other. If one of them realizes you are listening to each of them complain about the other, then you could easily lose both of them.

There is no best way or right way to cope in that situation. if it makes you feel uncomfortable you could tell them separately that you understand they feel stressed or bothered by mum\sister, but that you don't really want to get involved and that it might be useful or helpful for their relationship if they try to talk about their discrepancies and issues that they have with each other together, so they have the chance at building their relationship. (it might not work and they might not want to talk or work through their issues with each other, but at least they will understand you don't really want to play piggy in the middle with their issues.)

Sometimes it is best to have boundaries. If you feel uncomfortable with them speaking to you, about each other, simply tell them you are unable to deal with the emotional stress that causes for you.

If you don't feel comfortable listening to them talk about each other, you can always tell them that. Being the middle-man can often feel like you are choosing sides. Just like people who come to chat with listeners on 7 cups, they just want someone to vent to and listen to them about their frustrations. If you feel like you can't be that listener for them, which is totally okay, you can just tell them you don't feel comfortable and they will understand.