This is a long post but if you bear with me, you will understand why. There are a lot a factors that have played into where we are now and we are at the point that we need professional advice. Even if your advice is just what type of professional we need to see about this, it is much appreciated.
We have a Beagle/Basset Hound Mix, Female, Almost 6. We adopted her from a foster family 4 years ago and she has had separation anxiety since the day we got her. She was rescued from a puppy mill where she was kept in an above ground outdoor cage all day every day. My wife is a mental health therapist and wanted to use her for therapy dog work because of her usually calm demeanor (as long as we are around, she is calm. The second we leave, she freaks out). We put her through a few years of dog training which did wonders for her anxiety and now she has her CGC certificate. We almost had her anxiety under control, or at least calmed down quite a bit, but about 2 months ago we moved across the country from Pennsylvania to Oregon. Since then it has been chaos. She freaks out and randomly barks at almost everyone and every other dog in sight. Usually it is not a huge problem, the barking is not aggressive and she only barks until she gets the meet the person/dog but it is annoying none the less. She also barks a lot more during the day than she used to. She is crated during the day while we are at work and I stop in at lunch to let her out for a little bit. Whenever we come home, the barking is constant for a good 10-15 minutes. We have tried everything we can find on the internet. Leave her in her crate until she calms down, don't acknowledge her until she calms down, give her a chewy to give her something to relieve stress, play music to help her stay calm, etc. None of it seems to work. We've been trying to get her out more, go on more walks, go to the dog park, interact with other dogs which she seems to love, but it's still not helping with her anxiety. She still barks at other dogs constantly. Again usually not a problem but now she has started to lash out at other dogs, again nothing aggressive but it makes the other dog owners leery. Off the leash she's been fine, at the dog park she usually avoids the other dogs all together. She'll sniff them, maybe follows for a few seconds, and leave. Every once in a while if she sees a dog running, she'll even play chase but again not for long before she wanders off again. We just found a great dog park that is basically a wide open farm that she seems to love. She can run around without alot of other dogs to bother her. Today was also the first time that she showed any signs of aggression since we got her and it was at that same dog park. We let her off, she did her thing, met a few dogs, but mostly just ran through the field. We had been there about 30 mins when we stopped at a watering area with some kiddie pools. As she wandered in the shade, a bigger dog same up. Not sure what it was but probably some mix of a great dane and something else big. Again, usually not a big issue. When she first went up to the dog, her tail was up a wagging and she a goofy grin on her face, or at least as close as a dog can have. In a split second it changed. She nipped at the big dog's face and started barking and chasing the big dog. It took the other dog's owner jumping in her way and clapping loudly to make her stop and it took me running over and yelling practically yelling in her ear to break her out of it and look at me. It was honestly the only time we've ever seen her act like that and her barking sounded the most ferocious I've ever heard out of a dog who's usual sound is more of a howl. To be clear, me and my wife watched the whole time and the big dog did absolutely nothing to set her off, it didn't even flinch or jump until she nipped at it. At this point, we're too afraid to take her back until we get this figured out because we don't know what will set her off. My wife also can't use her for therapy work until we find a solution. But overall we want a happy life for our dog and we're pretty sure that the constant anxiety and stress is becoming a huge problem for our dog's health. Any advice is much appreciated. We have debated putting her on medication but are typically against just drugging our dog up to mask the issue. We'd like to find a more long term solution. Anything is appreciated, thanks.
TL/DR: We have a Beagle/Basset with severe anxiety. After moving across the country it has gotten much worse to the point of aggression towards another dog. What should we do or who can we see about this?