serious question about compatibility of DD1 and puppy

[rhetorician]

The puppy is 18 weeks old and in many ways a pretty good dog. She is a min pin terrier x and has strong territorial instincts, prey drive, etc. I have worked very hard with her on obedience and we are doing well. However, and this is a very big however, my DD1's responses to her are causing significant difficulty. DD1 really likes the dog and ddog is actually very tolerant - she gets picked up a fair bit, DD1 plays chasing games with her (which make her very over excited), but at times DD1 just provokes her. So we have a perfectly calm day with the dog, DD1 comes home and within minutes ddog is leaping up and snapping.

I think the stress produced by being approached in ways that ddog is not comfortable with has led to some fairly powerful resource guarding behaviour that we are tackling by not allowing her the things she tends to guard (bones, dog treats, occasionally food dropped on the floor) and insisting that she only eats her own food. But when she guards something it's full on growling, snarling, biting and it really worries and alarms me. I have a DD2 who has the sense to back off and read the dog's signals, but DD1 is seemingly unable to do this (this is a larger issue for her more generally).

I am seeing my dog trainer 1:1 to see how to deal with this, but my fear is that if DD1 cannot control herself around the dog and follow the rules consistently that this is profoundly unfair to the dog who will end up behaving in ways that mean we will have to get rid of the dog. This is not in any sense the dog's fault (so just now, literally this minute DD1 has gone up to dog's crate and she is growling). I am at my wit's end with DD1 - I cannot get through to her that she needs to back off and let the dog come to her.

oh DD1 is 6 going on 7, and dd2 is nearly 4

Have you actually told your dd that if she doesn't stick to the rules that the dog will have to go ,because I think that's where I would start. I would also find some child friendly trainer that will do training with your dd and the dog so that it's someone else showing her how to behave with the dog / teach the dog stuff rather than it just being you .

Yes, I have told her that. I brought her to the first puppy training class with me, but she was so distracted and bored by the necessity of consistency that I didn't bring her again - not fair to the other people there. She is not great on actions and consequences, as you can probably tell.

At one point my daughter was play inappropriate games with are dog which encouraged him to place teeth lightly on human flesh, something which is unacceptable in my view.
Like your daughter she would not listen, so I sat her down and took her through the consequences of ultimately the dog biting and I was very hard (she was 7) I pointed out that we could be forced to have him euthanased and that she would be at least partly responsible for his death.
It worked the inappropriate games stopped and 5 years later we all live happily together.

yes, I think we need to come the heavy on it - the last thing she wants is to lose the dog - she's rather like a puppy herself, come to think of it. I think a dog exclusion zone round her crate might work, as would a "take 5" when things get too exciting - "time out" is too negative (not that the dog cares). In many ways ddog is great - fine with being handled, reasonably obedient for a 4 month old, ok with other dogs terrible with the cat who would be delighted to get her rehomed I really want to work it through - the dog will be good for dd plus I really really like her