Hi,I am not a WDW employee but am the mom of an almost 16 year old daughter. (and an overprotective mom at that, according to her).
Last October when she had just turned 15 we went to WDW and we did let her go off on her own. Most of the times we were in the same park, but she just did not want to do hte same things we did. Now, this was our 7th trip, so she knows her way around very well. We stayed at POR and a couple of times she stayed back at MK while we went back to the resort. It worked out just fine. She knew where to catch the bus when it was time to leave. One thing that helped was she had her cell phone and we could call her or she could call us to see where she was.
I'd think as long as your daughters know they MUST stay together, and that their oldest sister has the final word, I'd feel fine with it. And I am a worrying kind of mom, too, but really it worked out very well. Oh yes, we only did this during the day, not after dark.
Good luck.