Splitting Advice

Why put them in your barn? Sealing them for a week prevents them from foraging, eliminating waste, and makes it much more difficult for them to manage hive temperature. Also, instead of disrupting them after a week by transferring into another hive body, why not start the nuc in the 10 frame equipment in the first place? Borrow the frame of honey, frame of pollen, and a couple of frames of brood (with clinging nurse bees) for each split, then ideally place them in the hive body in the location where you want them to establish. (Every time you move them you're going to lose some foragers and set them back).

With a hot, dry summer still upon us, 1:1 feed provides more water (which they can use to cool the hive), and is probably an advantage in this situation over 2:1 sugar water. After you add the queen (make sure the candy is not blocked by a cork), disturb them as little as possible, with a quick check after 4 or 5 days to make sure they released her from the cage. Then (except for topping up the feeder) leave them alone for a couple of weeks before checking to see how the new queen is laying.

Since they will have virtually no guard bees (since the adult bees on the borrowed frames are mostly nurse bees) don't forget to reduce the entrance to protect from robbing until they get more established, and make sure to use a top feeder instead of an entrance feeder. (An entrance feeder is an open invitation for robbing)

Good luck!

Why not take 2 frames of capped brood and the bees on these frames from each hive (6 frames total) and put 3 frames into each nuc box? Then finish the nuc box with 1 frame honey/nectar and 1 frame with pollen.

The bees attached can free the queen. The soon-to-hatch capped brood will add population and leave a place for the queen to lay when she is released.

I would close the entrance to no more than 1" wide so the few bees there can defend it easier.

I would also put the nucs where I was going to have the hive in the long run.

I would also try to pull the bees in the middle of the day when most of the bees in the hive are the nurse bees and not contain a large number of foragers, as younger bees seem to accept queens more readily.

I would put the candy side up with room for the bees to get at it from the top.

As for feeding, pull your honey for the season from your established hives. Open feed 1:1 syrup instead of 2:1 and if the stronger hives get the feed, then pull the frames from them and give the nectar to your nucs as needed. This will eliminate the nucs being targeted for robbing plus they get comb as they need it. It's going to be tough to get new comb drawn in the nucs without a nectar flow and until the new hives have adequate population, they will be candidates for being robbed by stronger hives, especially if you are putting the feed to them.

I would suggest moving away from your apiary if possible. I've done two splits this summer and both times...had trouble with robbing. The robbing killed one split and I was able to save the other. I would research Robbing Screens. this unique lil device is easy to make. there are designs on this site here. I'd make one for each split you'll be doing and staple it to the front of you nuc so that if needed, all you have to do is flip it up and block the entrance. make sure they're protected against ants. Those pesky critters will also try and rob/kill your new hive. Ants killed one split i've done. They mass invade and start killing bees and pulling brood out. If your going to be feeding....make sure it's contained within the hive and not open at the entrance. (feeding will induce robbing also). also....after the split...expect them bees to be a lil onery..takes 3-5 days for them to settle down.
So..
1. move em if ya can
2. make robbing screens and have ready
3. protect against ants.
4.if feeding. have feeder that is contained within a hive box.
5. cross your fingers, say a quick prayer and hope for tha best!