I'm glad that things are improving between Beth and Luna...I was going to tell you that there is something about Green Cheek Conures, I swear there is. I have a female Australian Cattle Dog, Lola, who is just turning 5 now and who has been with me since she was about 10 weeks old. Cattle Dogs/Heelers are extremely loyal, one-person or one-family dogs, and extremely clingy, to the point that it's almost annoying...She's my second Cattle Dog, my first was also a female who lived with birds, and who lived to be just shy of 14. I got Lola first, at a time when I had no "pet" birds, only breeders, and then an elderly pug. After the pug passed-away, I stopped breeding birds and rehomed most of my breeders, and decided to again add a parrot to my family, as I hadn't had one since I was in college. So I brought home Duff, a female Cockatiel. No issues at all. Then I brought home Lita, a blue Quaker. No issues at all. Then I brought home Bowie, a male Yellow-Sided Green Cheek Conure...and then the extreme jealousy and the "scared" behavior from Lola started...Then I brought home Kane, a male Senegal parrot...no issues at all...Only with the Green Cheek!
Bowie has been a part of our family now for over 2 years, and still to this very day, Lola is not only obviously extremely jealous of him whenever he's on me, but she too acts as though she's afraid of Bowie, just as you describe Beth is of Luna (even if Bowie is just sitting on my shoulder minding his own business and Lola has her head on my lap getting scratched/petted, doesn't matter, she's still jealous of him)...Lola will back away from me when Bowie is with me, but she doesn't want to back away from me, so she does this thing where it's like she's "fighting with herself", that's the only way I can describe it. She tries to come to me, but she'll get near me and then her lips will curl-up in almost a snarl, she'll make a weird whimpering/whining sound, and then start backing away from me, but then usually she'll flop down on her back and start rolling around on the floor, as if she doesn't know whether to run away from Bowie or lay on my lap for attention. Though Lola hasn't ever snapped at Bowie or any of the other birds, or anyone for that matter, I certainly cannot allow them to be alone with each other...in fact, I don't even let Bowie go anywhere near her, even when I'm sitting right there with them...
****Before you posted your update about Beth improving and getting along better with Luna, I was going to tell you that you'd only had Luna in your home for a month, and that it was still a very new situation, and that it was just going to take time. A lot of the time in these types of situation, people "jump-the-gun" and make rash decisions that are unnecessary and that they'll regret, simply because they only want what is best and fair to both animals, when the reality of the situation is usually that it's just a very new situation and that it will resolve itself to a livable situation in time. Beth was the only other family member in your home and she had you all to herself since the day you brought her home. And dogs are creatures of habit, and they tend to get very upset with change, especially when that change is having to share both their home and their "person" with another family member (which can be another pet, or even another person, such as a new significant other, a new baby, etc.).
And that's the most-common situation where this occurs with a dog, when a couple has their first child. It's very common for a young couple to first get a puppy together as a couple, and that puppy/dog grows-up in the household with it's people alone, with no "competition" for attention or affection, and they typically have the run of the house, sleep in the bed of their people, go everywhere with their people, etc. And then suddenly, just one day out of nowhere, the couple bring home a new human baby that demands pretty much ALL of the people's time and attention, and the dog is lucky if they get a walk or a pet during the day. And in addition there are usually new rules in the house for the dog, such as certain rooms that are off-limits to them, they suddenly aren't going anywhere at all with their people because now they have to take the baby and they leave the dog at home alone, and the dog pretty much gets lost...And unfortunately, if you look at Craigslist at any given time, you're bound to find multiple ads in any location about a young-adult dog, usually between 2-4 years old, needing to be re-homed, due to "not getting along well with the new baby", or "we no longer have time for him after having our new baby", etc. I see it all the time, and honestly it makes me sad for everyone involved, but it also makes me angry...maybe that's me being selfish on the side of the dog, but it just doesn't seem right to me...Something else that really bothers me is that there are a few couples that I know that have done just this, re-homed a pet due to having a new baby, and in the case of each couple, they all ended-up going out and buying a new puppy within a year or two of re-homing their first dog, because "they wanted to get a puppy that their child can grow-up with"...Uhg.
The point that I'm trying to make (the long way round, lol) is that there is bound to be jealousy on the part of your dog due to your new bird, but it's still a very new situation, and as long as you can figure out a way for both of them to get the attention they need, it typically works itself out in time, once the dog realizes that the new bird is not going to "take their place" in the home. So you must have been doing a good job of proving this to Beth, because she's already started to come around.
****One point that needs to be stressed, even though things are improving over time, is that you need to make sure that you never become over-confident in Beth's behavior and attitude towards Luna, as the second you let your guard down might be the second that Beth decides to take a bite out of Luna. All dogs are "predators" of birds, and they all act on their natural instincts, sometimes without any control. And terriers are natural hunters, so you can never be too careful about making sure that Luna is never out in the house with Beth alone or unsupervised, as this likely would not end well.
