Several years ago, I went through a season splitting like crazy in an effort to eliminate swarming (cough, cough). I trashed my honey production, but the trade off was learning about splitting, how long it takes for new queens to mate, and most importantly - laying workers and how nasty they are.
In several hives, for various reasons, the virgin queen was delayed in mating. I witnessed the virgin queen start to lay eggs on one side of a hive at the same time laying workers kicked in on the other. In every case that year, the laying workers tracked down the new queen and killed her.
My biggest lesson was the value of pheromones from open larvae to deter the laying workers and buy my new queens some time.
There are exceptions to every rule, and I can only hope that your new queen is okay. But what I worry about is that, like my hives that summer past, she got to lay a few eggs before the laying workers got to her, which is why there is some worker brood.