Your DD had a very traumatic childhood, one which will probably impact on her mental health for the rest of her life, sorry if that sounds a little bit hopeless. Your own struggles and grief are, I'm afraid, irrelevant to her. She may feel empathy and sympathy for what you went through, but that doesn't change what she went through, and certainly doesn't lessen its impact. She is grieving for that little girl who lost a father figure, and didn't have a biological father around very much.
I very much agree with the PPs that talk about the Parent-Child communication needing to change to Adult-Adult. I think this is very hard for some parents and children to do. We all have our opinions on raising children, and sometimes grandparents feel that they should share those opinions. Please be aware of (and try to remember back yourself to) how sensitive parents are to the opinions of their own parents on how good a job they are doing in raising their children. You may not mean it as criticism, but that sure as houses is what she's hearing it as. I wonder if this isn't just limited to the texts about her DCs and in fact she often feels criticised by you? The wedding dress situation makes me think that she wanted her mum there on the one hand, but then thought about it and didn't want it spoilt by feeling upset and disappointed if it hadn't gone as well as she'd hoped. I completely get this - I had a difficult childhood with a critical father who 'meant well' and I often felt disappointed when what should have been a nice ocassion didn't turn out that way, so now I don't generally look forward to anything and I'd rather be on my own, that way I can't be disappointed and I only have myself to blame if it goes wrong.
I suppose what I'm saying without meaning to upset you is that you have to at least consider the part you play in the relationship you have. It doesn't make you a bad person, certainly not a bad parent, but if you were two unrelated adults then would you get on? Would you put up with this from any other adult, but also would she? People have suggested a fresh start on her wedding day, but I think what you need is a bit of a break from each other, and then try to build something different. I realise that's hard when you want to continue seeing your GC as you are, but that may also have to change.
I do think a wedding is a perfect opportunity for you to tell her how proud you are of her, for all that she has achieved despite what you know was an incredibly difficult childhood, that you love her and you always will. That you know sometimes you come across as critical, but you hope she knows that you do it because of your love for her and your grandchildren, and you're trying harder to be supportive without coming across as judgemental, because you don't mean to be. The main message is that you are proud of her. What you don't do is dwell on 'poor you' or mention the gratitude you feel she should have for everything you've done - no.
If you think it will be hard for you to say all of this, or she might not listen and let you get to the end of what you want to say, then you could writer her a letter. Again I think a wedding is the perfect opportunity to give her such a letter, it won't seem odd, in fact its very appropriate. A marriage is traditionally when parents hands over a child to their new spouse, you are letting go, its the right time.
The risk of stepping back and letting her decide when to contact you is that she then misinterprets this as you being uninterested. What ever happens, please, please, continue to show uncritical caring interest in her children and her life. So: "What are you/they doing?" and then if she replies "Oh that's great, how wonderful, good for you/them!" or "Oh dear, that's a shame, I hope you're ok?" Try to keep your own anger and frustration to yourself if she decides to 'grey rock' you sometimes, she might need to do that for own sanity.
And the lying... I don't know but one thing I've noticed with children whose parents have divorced at primary school age is they do seem to lose their moral compass a bit. I am generalising, but when I think of the children that my DDs have had issues with because they've lied, that seems to be a common theme. I've wondered if this is because they see their parents lying to each other, or lying to them about what's going on, or because they feel that they can't be entirely honest with one parent about the other, and because of their age the lines get blurred so they lie more in general. She may have grown out of it, but due to the additional trauma when she was 13, perhaps it became more ingrained and the lies just got bigger. Its definitely for attention, but it is an interesting psychology when people seem to believe their own lies, or can deny having told one as if they truely have forgotten that they said it.
My DM once told me that their parents happiness is not a child's responsibility. I was feeling guilty about the failed relationship with my father. As a parent, you bring your DCs up the best you can and then you let them go to make their own successes and mistakes. You hope they'll want to have a relationship with you, but they may not and they don't have to. Actually we are all responsible for our own happiness, but you do come across as wanting her to act a certain way with you because you've always done everything you can to make her happy. Is she acting very entitled? Yes. Do I blame her? No. She had a shitty deal, she's still angry, and you don't make up for that loss. You can't.
One question - does she still have a relationship with her biological father? Sorry if I missed that.