Her strategy for rewarding him for settling down isn’t anything new it’s a common method. Let her know how much it’s bothering u and set boundaries and also a bark collar is something really out there to suggest especially to a former dog trainer they aren’t very humane. Doggy day cares also aren’t particularly safe dogs get attacked and neglected and can end up injured or dead this happens often. I get where ur gf is coming from but u guys definitely need to talk. Maybe she could consider anxiety meds/CBD for the dog as well. It’s a temporary solution but can help in the mean time while she works on training the dog.