+1 on this. For whatever reason, it is very common for packages to supercede their queens.Supercedure is common enough with package bees, queen may be in the cage for up to a week depending on how long the supplier had them packaged, picked up by your retailer or you, introduced to your hive, the 3-4 days for her to get out. By that time, workers may decide something just isnt right with her. Check for larvae, sometimes you only have empty cups.
The Split described is easy as falling off a log, and many have broken their legs doing so. When we offer advice to a new beekeeper we must take a great deal into account. We often incorporate personal experiences into our advice as that is the basis of our knowledge. However not all factors in the equation have the same value. a single frame split from a package although slow growing in has a chance of making it in Alabama, However, in Indiana it has little chance as mathematically it cannot become strong enough to develop resources to survive the average winter. The beekeeper can with knowledge and effort create conditions that will enable the hive to do so. Understanding of forager/nurse bee behavior is not always engrained into beginners and as such a split often goes without foragers for a significant time, further stifling the production of the queen within the split. While at the sane time completely ceasing production within the main hive. These are not insurmountable problems, and certainly problems that can be dealt with by the bees more easily in latitudes where wither is more temperate.Tenbears, making a split like I suggested is perhaps more simple than falling off a log. I don't see anything ridiculous about my suggestion. I wish someone would have suggested for me to make a split last year when I found the same thing. If the bees want to supercede, then I think the OP should let them, BUT there is no reason to allow them to take out a perfectly good queen in the process. If the queen is marked then all the OP has to do is remove one frame from their hive and place it in a nuc box. It took me a year to figure out that this ISN'T rocket science.