I don't think you got the queen from the swarm you caught. By now it is laying worker and IMO not worth keeping. I would just dump the hive and use the equipment for a split of package.
I think the main concern here is re: the mated queen purchased for that swarm ... ?
Davers - Mated Queens are either received by a colony with 'open arms' or with aggression. Usually, it's immediate aggression followed by acceptance after a few days.
What's unusual here is the 'little attention' which was being shown to that Queen. I've only ever seen a Mated Queen ignored just the once, and a very strange sight it was too - in my case it was a queen purchased at some expense (wouldn't you know ... ?) - and yeh, just try getting a refund.
She was met with total indifference - the support bees in the mailing cage received more interest than she did. I eventually released her, to 'take her chances', but she was never seen again. Hardly surprising.
These days, whenever I come across a weird situation, I like to get back to 'known conditions': is there a queen present ?; if so, in which box ?; is she laying ? - and so on. I don't much like working with the 'maybe there's still a queen in there'-type scenario.
So - what I'd do in your situation is shake those bees out into another box, through a queen excluder, and if that queen is still there, then remove her.
Also - right now I'd check VERY carefully for the presence of eggs of laying workers, as that colony has been without brood for some time. Murphy's Law says workers will start laying the very day before you introduce your frame of open larvae !
Then - on a nice sunny day - swift a frame of BIAS over to that (now confirmed queenless) colony. If you can transport it in (say) an expanded polystyrene box, all the better. Supplying warmth shouldn't be necessary in a warm vehicle on a warm day, but a damp towel or similar inside the box to maintain humidity would certainly be a good idea.
Good luck
LJ