My daughter and I have had difficulties in the past that sound similar to what you're describing. Based on my experiences I would guess that in part you've become the target for frustration over how her life is going. She knows that you will love her no matter what.
I discovered over time that part of my daughter's difficulty with me is that I was too involved in her life. I, too, cleaned and helped with housework. She seemed to take my help for granted. She finally told me that it was her house and she didn't want me to do her housework. Now, a couple of years later, she will ask me for held and expresses appreciation. And I can ask if she wants help and she will say yes or no.
I learned to not get involved in anything unless she asked me to get involved. That was a very difficult transition for me. I'm a problem solver and helper. Helping came naturally for me. I learned that my always being ready and willing to help was keeping us from developing good boundaries.
I suggest that boundaries are an issue for you too because she is keeping away from you. That is the ultimate boundary and sometimes has to be done before two people can get back together in a healthier way.
I think I understand your pain. I felt rejected, unappreciated and unloved. You've tried to not say anything when you've been concerned. I suggest that much of this anger has built up over time because the two of you haven't talked about how you were feeling as you went along.
Perhaps now you feel angry because you tried so hard and it didn't work. And it feels like she'll never come around to share your love again.
There is hope. Both of you will work this out. I suggest she does need this space to discover who she is without you and you need the space to find a way to feel a part of her life without being so involved. You will rebuild your relationship based on honesty.
Honesty is difficult. We have to know when to talk about something and when to be quiet. You were right to not talk about her parenting style. It isn't your business. I suggest it's best to not ask questions based on your grandchildren's conversations with you. Their relationship with their mother is also none of your business. That was a really difficult lesson for me to learn.
And so I've become a listener mostly. Most of the time I see my daughter's and my grandchildren's conversations as a way for them to vent. I work at not getting involved in solving a problem, tho I'll make observations about how relationships work and how the child might do things differently if they ask for this information. I'll make suggestions to my daughter only if she asks me outright for my ideas. I present this information as ideas only.
Earlier I probably would've done the same as you did with your 16 yo granddaughter. Now, I hope that I would take her back home and tell her she has to do what her parent's told her to do. I would sympathize with her but I would also tell her this is something she has to work out with her mother.
I think the incident with your granddaughter is why your daughter is so angry. The fact that she wouldn't let your granddaughter say good bye or get her things tells me she was very angry then. And when you e-mailed her she became even more angry. It probably felt to her that you were interfering. And if she knows you took your granddaughter's purse to her and took her to lunch she would be even more angry. I suspect she knows because how else would your granddaughter get her purse. Your actions felt to her that you were supporting your granddaughter and not her. Because you asked in e-mail, she had only the words to figure out how you felt. I've found that it's best to not talk about potentially misunderstood things in writing because they are usually misunderstood.
Because of her anger she is overstating everything when she makes accusations. I learned in therapy that when someone says "you always" or "you never" it is their anger talking and is totally unrelated to how they would feel if they weren't angry.
You are hurting big time but you may have to wait until she calms down. She will eventually talk with you. In the old days, I would write to my daughter and apologize. She rarely accepted my apology nor did she mention it later when she did call to tell me to never do "that" again. I would then apologize in person and it was usually a beginning to our rebuilding our relationship.
I did feel better after having written the apology once I accepted that I was writing it for my benefit without expecting a response from her. I learned to not mention anything about how she hurt me. I would tell her that I loved her, missed her, and was hoping that we could get together again soon.
This, too, will pass tho I'm sure it doesn't feel like it. What is happening is a normal part of maintaining relationships as circumstances change. As you mentioned she is having difficulties that influence how she thinks of what you do and say.