I think it depends on the context op.
I agree with you that it’s awful when someone gets defensive and turns an argument around on to you. You can’t make progress in your relationship that way.
Equally though, say if I was tired and snappy with my dc, or a friend, and then my dh criticised me for it, I might be accepting of that criticism if he had stepped up all week and done half of all of the work involved in running a family home and looking after the dc.
But if I had done the majority of the school runs, house cleaning, food shopping, homework supervision, evening meals, packed lunches, taking dc to extra curricular classes, dog walking, laundry etc etc, as well as working full time, and then my dh criticised me for being tired and snappy; frankly I would be less than impressed.
Instead of criticising her, why not bring her a glass of wine or a cup of tea and be gentle and give her a hug and ask her if anything is bothering her? Ask and listen. If appropriate, ask if there is anything you can do but don’t jump in to Mr Fixit mode immediately. Just listen and sympathise. And if she asks why you are asking, then you can say you noticed that she was a bit off with her friend and the dc, but don’t say it like you are her enemy.
Try and understand her perspective about the dc in particular and don’t become referee or judge and jury.
Also, look to your own behaviour and see how often you get tired and snappy too, as no ones likes a hypocrite.
She may be under pressure at work, have something going on with her family, be feeling physically unwell with her periods or be pre-menopausal. Cut her some slack and come at this from a perspective of genuine empathy and not one of judgement and maybe see how that works instead? You are on her team remember.