When doing a fly back split with intent of making nucs, I prefer a two step process. Step one is to make the flyback as you described, moving the entire original hive to another location in your yard. You can even place it next to the flyback. Wait 10 days and THEN make your nucs with the frames containing the queen cells the still strong hive full of nurse bees has made. You get better fed queens this way. Divide up the remaining resources, bees, capped brood, frames, etc. as you see fit, but make sure each nuc gets plenty of stores.
Oops, just realized you were leaving eggs with the queen. Give her just one frame of capped brood and one partial frame of honey. Leave all the eggs in the original hive.
Thankfully, the bees are smarter than I am. They are doing well, in spite of my efforts to help them.