Autosomal DNA matches for me

I was chatting with a buddy of mine who has a participant in Hawkins yDNA group #1 which is my group (my dad tested for me).  She was asking me about the FF test.  She wanted to know if I had any Hawkins matches on my FF .....I took a look......and lo and behold, I had one match with a lady who has maiden name Hawkins.  As we chatted, I learned that her Hawkins line connects with yDNA family group #3 while mine connects with family group #1.  These groups are clearly different from one another.  It is not on our Hawkins lines that we match.

Then we looked at our Moore lines.  Again it is probably NOT the Moore line that is our connection.  

This lady does not match my mother's FF test, thus it is likely that we connect somewhere in my father's ancestry.  So here is quick run down on my ancestry that is on my dad's side for Lois and Elaine to scan:


My Hawkins line probably lived in the Northern Neck as early as late 1600's.....then moved up the Rappahannock River to the Culpeper/Orange County area of Virginia.  When most of these Hawkins lines moved on to Kentucky after the Revolutionary War, my own line remained in Orange and Louisa Counties until the late 1800s when they moved to Huntington, WV (where I live now) for railroad jobs.  I am fourth generation Hawkins in Huntington and have lived here all of my life. Other surnames that were associated with this Hawkins line are:  Pinkard, Anderson, Carter, Farrar, Scott, Lacey, Johnston, Burnley

My great-grandmother on my Hawkins side was a Beuhring.  This family had been Burig (with an umlaut over the u) in Germany.  FGL Beuhring moved from Germany to Baltimore MD before the War of 1812 where he married Frances Eleanor Dannenburg whose ancestors carried surnames of Konig from Hamburg Germany and Dannenburg from St. Petersburg Russia.  There is the possibility that there were surnames Schultze and Mayer in earlier generations.  

Other ancestors of my gr-grandmother, Beuhring were:   Mueller/Miller (descendants of Jacob Mueller who was the founder of what is now Woodstock, Virginia in the Shenandoah Valley), Chapman, Holderby (from the area around the York River in Virginia), Pendleton from the same area, possibly Macon, Pollard, Pannell, Hurt, Douglas, Bell, Camden from very early Virginia....Clendenin, Wiseman, Handley who likely were Scotch-Irish. 

On my father's mother's side are the surnames:  McGregor, McKinsey, Hare, Slater, Chapman/Redmon, Fresch, Elliott, Moore, Lackey/Leakey, Maynard, Jenkins, Cureton,