Hi fruitloop
I think the original nuc sounds to me like a second hand car purchase - you can never be quite sure what the last owner did. It sounds like it never properly got out of the blocks, two frames of brood in its first year is really unimpressive. Was it from a local supplier or a main dealer?
The increasing price of nucs commercially has encouraged others to make up and sell boxes of bees as sideline and their idea of what constitutes a reasonable unit varies. The BBKA published a guidance note a while back with pointers
https://www.inibeekeepers.com/cms/wp-content/uploads/2018/06/nucleus_standard-l014_1342859848.pdf
If it was a commercial supplier who also sells Queens, I think I would be in touch with them. If it was a local and I got it cheap enough, maybe put it down to experience - a less scrupulous beekeeper will probably (unfairly) blame it on you anyway. Some people hive swarms and sell them on as nucs but unless it is a caste headed by a virgin, the Queen is probably by definition past her best. I have also heard of people taking a failing queen and just putting them in a smaller box - Taraaa! - a nuc to lumber a beginner with. Doesn't sound like the queen is marked either - another shonky move by the seller.
Good advice from others, bung it in your nuc and look for ways to requeen. You could put your now empty hive on the shed or garage roof as a bait hive with a couple of the drawn combs you have left over. You still have a good chance of picking up a free swarm or even better a caste with a virgin and then can unite to that and go into winter with a viable unit. If your better one tries to swarm, don't be in too much of a hurry to knock down cells but see them as a requeening opportunity also -your colony sounds like a good candidate for a forced supersedure (which put simply is introducing a sealed queen cell wrapped in foil into a failing queenright colony), doesn't always work but when it does it's like magic.