I'm new to making nucs, too.
I made some nucs with swarm cells this year and they are doing well. I made them up with three frames of capped brood, one frame of honey, one empty frame. I made sure there was pollen in there too, and I shook some extra young bees in too. I used 5 frame deep nuc boxes. I wasn't sure what size you were using?
A new nuc isn't in a great position to rear a queen. They have to feed it properly and keep it warm/cool enough. Better to give a queen or a queen cell to the nuc.
Your capped bees might have died if they got too cold (or too hot? ) because of not enough bees in there looking after them?
I don't think you'd introduce disease by making a split like this. I guess you have to choose, are you going to persevere with this nuc (give them more brood, bees, and a queen or the eggs/larvae to make a queen) or are you going to combine them back into the strong hive?
Also, welcome to the forum. Why not post an in introduction in the Welcome forum, and put your location in your profile.