Small queen and pollen trap

I'm not sure about weather she was mated or not, but I've had the "ball of bees out on the ground", surrounding the queen before. I've placed her back in the hive, but found her missing days later. So it sounds like she may have been rejected, and what you were seeing was her being balled by colony members. Sounds like you succeeded in rescuing her, good job. I like your idea of starting a new nuc from another hive and introducing her a second time. Hopefully this works for her sake... you can always recombine later if it doesn't. If she was virgin, however, she may have missed her opportunity to mate. They typically will mate within 3 or 4 days of hatching. I guess I'm not sure what exactly happens if she misses this window, weather she just doesn't get mated properly or not at all, but everything I've read, pretty much indicates that it is critical that she mate within her first week. Other than getting her into a colony and seeing her produce eggs and normal brood, I'm not aware of any other way to evaluate her worth... If she failed to be accepted again, I would just consider that nature is pretty good at vetting out problems, so the bees must know something we cannot detect. Get a new queen at that point. A queen hungry nuc otta accept her. I would also ensure there is some candy in her cage, and put a drop of water on the screen daily for them to drink.