Show her mistake and just do this matter a factly.

Hi Irene, I’m guessing your parents are reasonably elderly and unfortunately some can become fairly fixed in how they do things. Its hard to change and admit you might be wrong.
Its made more difficult because I suspect your mom is feeling little bit out of her depth and is reluctant to admit it to you. So you are on the back foot unfortunately.
If you can find a way to help her ‘save face’ such as admitting she is facing a difficult problem and suggesting ways to handle it rather than doing it for her. Try to be her helpful coach rather than the one who solves the problem. None of us likes to feel inadequate so helping her is the way to go I suspect. Try to have a conversation with her away from your father’s ears about how to handle different situations!

In their world they are always right - no use arguing with him. My husband refuses to believe me when I contradict him which I don't do anymore. Just agree.

I know the feeling my mum is the same it doesn’t matter what you say to her she will tell home off or get angry I know it’s hurting them but dad doesn’t know he is doing it I am getting someone in to talk with Mum

Why bother at all? Just agree with all that is said because it will all be forgotten in moments anyway. I just say 'whatever you say' and leave. Moments later, I will ask who wants a coffee? and it's all forgotten. I hate confrontation and stress, so will move heaven and earth to avoid it, but feel all the better for doing so. Win win situation or what? Try it, I can almost guarantee you will both benefit. x