I am looking at the options to self-publish a children's illustrated book, but I cannot find up-to-date info on KDP Kids, as most threads I find go back to 2013. If I use this method, will I have the option to offer print copies as well as kindle versions?
There's a fixed-format kids book creator for an ebook, but the file that it puts out is specifically for an ebook. You would have to format the pdf for a print book separately, though the process would be very similar. Several points on kids' books:
Print is more likely to sell than ebook format, but the market is saturated, so sales will be very small.
Make your print version through CreateSpace, not KDP-print, for the many reasons you'll find all over the forums.
Color in print will skyrocket your price.