It sounds like the queen intro into the nuc is going fine. Leave them alone 7 to 10 days. However, my question is why did you set the old queen aside. You do not like her performance, she is of the swarmy mediocre genetics you are trying to get rid of in that hive and the others (4). Just go kill her now, like right now, and combine those resources (bees etc) into the other hives than can benefit from them.
On hive 4. Glad you did not put the queen in yet. Because if you did the bees will assuredly kill her. Not because they are pissy, but because of the condition of the hive you described. There is high likelihood that there is a virgin(s) running around in there right now just looking for a fight. In this case, here is what I would do: Leave hive 4 alone for now. You will see why in a few moments along below.
Virgins are hard to find and are extremely disruptive to the beekeepers plans. They can be dealt with by method of time or by advanced queen finding techniques. In your case, lets choose to use time as it is the easiest and has no detriments to the end result of having your hives requeened and advancing.
Leave that 2nd new queen (4s new queen) in a nuc and proceed to get her introduced and laying in the nuc. This gets her established and smelling good while in a safe place. Leave her in there for 2 weeks. The end result, the end hive, will be advancing in parallel as she will be combined later.
Wait and monitor hive 4 for 2 weeks. At that time go looking for evidence of a queen. (eggs, larvae). At that time you should be able to find her and promptly kill her. If there is no evidence of a queen, even better, you can proceed with your tear it down plan by removing the hive and distributing the resources to other hives, including moving that new queen in the nuc up into a full box and placing her box where hive 4 was and had been removed from.
To introduce that new nuc queen into the hive 4 after you have killed their queen, there are two very high success methods you can use. One is by using a push in cage. You can google that method rather than my describe in detail here. The second is by inserting the whole nuc into the hive. My preference is the nuc intro method for established queens. There is no need to wait more than an hour or so after killing the undesirable queen. Kill her, go have a coffee, then go back to the hive and requeen it.
To do the nuc insert method, make sure it is a nice warm sunny day with no thunderstorms to well up on you. Goto the hive 4. Open the hive and spread the boxes, with no covers, so all are fully exposed to air and sun. Go into the bottom brood box and from one side of the box, furthest from the entrance if you have reducer on, remove the number of frames that coincides to the size of the nuc being used. Leave the hive open and spread out like that for 20-30 minutes, exposed to air and sun. Now go get the nuc and insert it as a frame-pack into the open space you made in the bottom box. Ensure the frame the queen is on is placed in #2 position, near one side of the box. If you are really worried about her safety, put a push-in cage over her as well. Leave the hive open for another 10-20 minutes. You can be cleaning up the other stuff around your bee yard while you are waiting for the bees to settle. Proceed to put everything back together and close up. Leave them alone for 1 week. It should be smooth sailing from there on.
Bottom line, do not requeen 4 just yet. Unless you know how to find and deal with virgin queens.
Hope that helps!