There's some problems going in my family and I want to solve them by talking to my mother about them, but I know that it will most likely turn into an argument and she will probably heat it up.

What's the best way to argue in such situations? If she gets mad and argues louder, what would the appropriate response be? If she doesn't follow logic, what would be the best way to convince her?

Asking here because I need some advice from a TRP perspective. I know she's wrong and I know why. But saying it to her might not help, so I need a better way.