All of the information you provided regarding Rebecca HAUGHT and her sons jibes with the information I had found. Unfortunately, my proof that Nicholas HAUGHT was her husband and father of Charles and Daniel Curtis is somewhat indirect, although I feel rather strongly correct.
By going through the 1860 Springhill Census by hand, I found a Nicholas and Rebecca HART living in Springhill with two sons, Curtis and Charles; all the right ages. And, to top it off, Rebecca's daughter Nancy (my direct relative) from her first marriage, was living with them; again with the correct age! The census suggests that Nicholas was born in VA, but I believe the Springhill area of Fayette County was once part of VA.
Nicholas was quite a bit older than Rebecca so I suspect that Rebecca was at least a second wife. Rebecca's first husband, Andrew Lancaster, died in 1850.
So, what do you think? Thanks so much for help with this!