i had this same situation two weeks ago, here is what i did:
i picked up the queenless hive and took it about 70-80 yds away and brushed off ALL the bees onto the ground, one frame at a time. i placed the hive back in its place and put another super on top of that for the nuc frames, with a piece of news paper in between the boxes, then covered them up. you will need to provide a top entrance for the nuc bees. within two days all was fine. this is the procedure a professional beekeeper outlined for me, although he doesnt dump the bees. this is what worked for me the one and only time i have had this problem.
others on this forum say that they wouldnt risk the healthy hive in this situation, fearing that the laying worker hive can overwhelm the queen, and that this method works only half of the time. im not doubting what they say but i had good luck doing this and this pro that i talked to was very confident that this would work.