Hi Stormy Faw,
I hope you are half as impressed as I am by your effort. It is no small feat to trace the records about someone with a common surname, especially when the given name seems to change with each new find. Bravo!
You asked, "do I have a case?"
If you are asking whether or not all the records you have identified seem to be about members of the same family, I'd say yes. On the other hand, you may be asking if these records are sufficient from the standpoint of proving identity and kinship.
We don't all approach this work in the same way. I usually do a better job (including that my database doesn't get waaay out ahead of me) if I record indexed information along the way in the resarch notes, but base added links and relationships on information found in the underlying historical records (originals). From an extended group of records like this, the originals are bound to contain more genealogically valuable information, some of which might address the conflicts you've identified among the indexed items.
I tried to add links to some of the census images in the materials that follow. From the citations about the other indexed items, originals can probably be obtained via FamilySearch's Photoduplication Service
It can take a little time to gather those originals. I'd use that time to learn about other records that might give the story about this family a little body. For example:
Might we find the marriage records about Rainey and her husband? About Rainey's parents? 
How can we learn about the Laws interments at cemeteries in Beaver Creek and/or Boomer, including whether or not graves for Rainey's parents can be located? (I'm only guesing that there are not five different given names inscribed on the father's tombstone, but wouldn't it be fun if there were!)
Are there archives of the local newspapers published? What years do those cover? Does the local library or historical society have an obituary index or card file? Is it possible to discover obituaries about Rainey and her husband? About Rainey's parents?
Are there Laws family records available from one or more of the churches in the area of Beaver Creek and Boomer?
A couple of other notes follow. Again, really impressive work! Hope this helps.--GeneJ
A. About Rainey.
Great job pulling together the early records on a difficult name. Hoping we might find some first hand information, I tracked down the 1940 U.S. Census about her. This was interesting because the family was enumerated twice. She is marked as informant on one entry (at Moravian Falls, Wilkes); no one is marked as informant on the other (at Boomer, Wilkes--none of the households on that page have an identified informant). Sort of cool to compare data bits in the two records. Given the time period in which she lived, there is probably other first hand information about her. For the census, see
"United States Census, 1940," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/KW72-4M8 : accessed 2014), Raney Broyhill in household of Cicero Broyhill, Boomer Township, Wilkes, North Carolina, United States; citing enumeration district (ED) 97-3, sheet 12A, family 188, NARA digital publication of T627, roll 2988. Informant identified as Rainey Broyhill, wife.
"United States Census, 1940," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/KW7N-9W7 : accessed 2014), Rainey Broyhill in household of Cicero Broyhill, Moravian Falls, Moravian Falls Township, Wilkes, North Carolina, United States; citing enumeration district (ED) 97-13, sheet 17B, family 297, NARA digital publication of T627, roll 2988. From the census image, one Millard Laws, age 44 and widowed, resides one door down.
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