Dottie60 Welcome to Gnet!
I'm sorry to hear about this, it is obviously very painful for you.
I had 3DDs and teenage years were up and down as is normal. It sounds as if there is more than the teenage stuff here and that your DD and DGD really clash, your DD perhaps, finding her daughter very irritating and being unable to control how she feels. This is not at all uncommon, for a parent to find a particular child gets under their skin, no matter what their age.
It is possible your DD vents a bit more when you are around because your presence makes her feel a bit safer. But it is more likely that she has got into a pattern, and is unaware of how critical she is of her daughter. Would it be possible to have a word with her? Start by commiserating about how tough it is to have teenage children today - it really is much harder than ever before; very expensive and very nerve-wracking regarding the friends they might have and where they go. Maybe your daughter needs a self-esteem boost and is unconsciously projecting things onto her daughter. I would build up your daughter, say how well she manages and you respect her as well as love her. Then very gently say you can understand how hard it is not to be critical and have very high standards regarding the children, especially these days, but you think your DGD is getting affected by her criticism and losing her self-esteem. The best results are always obtained by praise, tell her, and point out your DGD's good traits and give your DD credit for raising her.
I am truly glad I am not a mother of a teenager now. I couldn't afford the mobile phone bills for a start! But the anxiety about the world today, the problems facing young people, the difficulties to get jobs, the loans and debts for university, it all is so daunting and frightening.
Can you take your DGD out for a day or have her over for a weekend? I realise she might prefer to be with her friends, but it might give her and her mum a bit of a break if they are getting on top of each other? Maybe it could be a regular thing, if that is possible.
Wishing you much happiness and hoping all will come through well for everybody.