Have you been professionally taught to use a hackamoore? If not, a lot of her neck carriage may be from rider error. I would advise in getting some formal training with her just to help her loosen up (it helps a LOT in the long run, especially as your daughter gets older and wants to ride harder/more often) If you can't do that, maybe some lessons for you would be a good idea, not to learn how to ride (since you say that you're confident in the saddle) but to learn about flexation exercises etc, that you can carry on to help Lola with.
Here are a few flexation and yielding videos that I found. Some of them aren't completely how I would do it, but they're good for basics.
On the ground:
I do NOT like part three of this series, as I think pulling on their tail and asking them to back is just rediculous, especially because pulling and pressure are COMPLETELY different. This can be dangerous as well. For this reason, if you do decide to follow his instructions in pt 3, do not think that I agree or recommend it.
I could give you dozens of explanations, links, and videos- but I really feel like if you don't know how to get her to flex/collect/yield, it's just an all around good idea to look into either a trainer or a riding instructor.