I believe your William is the brother of my Thomas. Here's what I've pieced together, some from Internet sources, others from research at FHC. I can't swear to it, of course, but I think this may be correct.
1-John Maxwell
b: in Ulster, Ireland
d: 1786 in , Rockbridge, VA
sp: Mary
m: 10 Jan 1726/27 in Downpatrick, Down, Ire
. . 2-Margaret Mary Maxwell
b: bef 1740
. . 2-John Maxwell
b: 1737 in , , IRE
d: 2 Jul 1819 in Lexington, , KY
. . 2-Thomas Maxwell
b: bef 1740
. . 2-William Maxwell
b: 1744
d: Dec 1820 in , Logan, KY
. . sp: Elizabeth Vansandt
. . . . 3-Mary Maxwell
. . . . 3-Margaret Maxwell
. . . . 3-John Maxwell
b: 1773
. . . . 3-James Maxwell
b: bet 1775 and 1780
. . . . 3-Elizabeth Maxwell
b: bet 1765 and 1784
. . . . 3-Rebecca Maxwell
b: bet 1765 and 1784
. . . . 3-Thomas Maxwell
b: bet 1784 and 1794
d: 1837 in , Logan, KY
. . . . 3-William Maxwell Jr.
b: bet 1784 and 1794
. . . . 3-Audley Maxwell
b: bet 1784 and 1794
. . . . 3-Rachel Maxwell
b: bet 1784 and 1794
. . 2-James Maxwell
b: bef 1745
d: bef 27 Mar 1821 in , Tazewell, VA
. . sp: Jane Roberts
b: in Philadelphia, Philadelphia, PA
m: in Philadelphia, Philadelphia, PA
d: aft 1820 in , Tazewell, VA
. . . . 3-Jennie Maxwell
b: in , , VA
d: abt 1782 in , Tazewell, VA
. . . . 3-Mattie Maxwell
b: in , , VA
d: abt 1782 in , Tazewell, VA
. . . . 3-Elizabeth Maxwell
b: 1767 in , Montgomery, VA
d: aft 1850 in , , VA
. . . . 3-John Maxwell
b: 1770
d: 1841 in , Wythe, VA
. . . . 3-Mary Maxwell
b: 1775 in , , VA
. . . . 3-Margaret Maxwell
b: bet 1776 and 1778 in , Montgomery, VA
d: 19 Dec 1851 in , Tazewell, VA
. . . . 3-James Maxwell
b: 1780
d: 1866
. . . . 3-Nancy Maxwell
b: 1780 in , , VA
. . . . 3-William Maxwell
b: 1782 in , , VA
d: 1868 in Pomeroy, Meigs, OH
. . . . 3-Robert Maxwell
b: 5 Jul 1786 in , , VA
d: 20 Apr 1861 in , Linn, MO
. . . . 3-Jane Maxwell
b: 13 Mar 1788 in , , VA
d: 20 Feb 1861 in , Pike, VA
. . 2-Thomas Maxwell
b: bef 28 Feb 1747/48
d: May 1781 in , , VA
. . sp: Rebecca (Maxwell 650) UNKNOWN
. . . . 3-Mary Maxwell
b: in , Montgomery, VA
. . . . 3-Sidney Maxwell
b: abt 1770 in , Montgomery, VA
. . . . 3-Sara Maxwell
b: abt 1776 in , Montgomery, VA
. . 2-Audley Campbell Maxwell
b: 15 May 1761 in , , VA
d: 4 Mar 1835 in Tazewell, Tazewell, VA
. . sp: Ann Matthews
b: abt 1764 in , , VA
m: 30 Dec 1780 in , Rockbridge, VA
d: abt 1820 in , Tazewell, VA
. . . . 3-John Maxwell
b: 6 Apr 1788 in , , VA
d: 1850 in , Pike, VA
. . . . 3-Elizabeth Maxwell
b: 12 Feb 1786 in , Rockbridge, VA
d: 14 May 1857 in , Raleigh, VA
. . . . 3-Thomas Maxwell
. . . . 3-Jane Maxwell
. . . . 3-Audley C. Maxwell
d: abt 1837 in , Tazewell, VA
. . . . 3-Rebecca Maxwell
b: 31 May 1790 in , Tazewell, VA
d: 25 Sep 1853 in , Shelby, OH
. . . . 3-Joseph Maxwell
b: 18 Sep 1800 in , Tazewell, VA
d: 20 May 1882 in , Fannin, TX
. . . . 3-Sarah Maxwell
b: abt 1808 in , Tazewell, VA
. . . . 3-William M Maxwell
b: 24 Oct 1811 in , Tazewell, VA
d: 8 Aug 1892 in Brookfield, Linn, MO