Hi Jenny well, where do I start? This sounds very familiar to me. I have a rollercoaster of a son, nearly 19 years old who, one minute will be the funniest, kind, caring, loving son I could ever wish for, and the next minute he will be sarcastic, rude, obnoxious, verbally offensive, storming around that I wish the door would open and a huge pole would grab him and take him somewhere else!
I have been to hell and back with him over the years, taking what he has said to heart, being upset, shocked, trying to get him to see counsellors, worrying until my hair is now grey and sparser than what it was. It has all got me nowhere, to be honest and now I deal with him by simply ignoring him if he starts. If I tell him to go upstairs if he starts picking for a fight and wont, then I get up and move. He usually then moves as he has noone to impress or try to get attention off.
I know you DGD has a lot going on but other people have their mum remarry and survive. I do think that at this age they will try to pick on something to get angry with as their hormones are raging and it comes out to the one person they know they can get away with it with.
You need to take as little notice of her as possible once she starts to put you down, rise above it. You know you are intelligent, kind, caring, you don't need a 18 year old to confirm it. She will do one day, just not now. Find some place where you can be away from her (not on the moon!), maybe your bedroom or lock the bathroom door and take a long soak. Lay down the ground rules. Tell her that if she starts to go too far she is to go to her room and stay there until she calms down. No banging doors etc. Treat her like she is having a tantrum. We do make allowances for toddlers but teens we expect to behave themselves all the time and it just is not going to happen. If a toddler started a tantrum, you wouldn't carry on having a conversation with them or trying to reason, you would walk away until they calmed down. So do the same with your DGD. It works with my son. You do need to explain to her that you deserve respect, that you have brought up a family and are not stupid, and that if she starts to make you feel so, then get up and move away from her, go and make a brew, don't take it, don't give her an audience, which is what she wants. If she follows, go to the toilet and lock the door, take a book. When you come out, hopefully she will have moved onto looking on facebook or something.
PM me if you want. It is not easy but she does need to know that you are going to be there for her but there are boundaries. Just like in life. Good luck. 