I looked at your timeline some more, and I think the information below is what you’re proposing. It works well enough, but I don’t see any support for the birthdates of the children in the Pittman report. They might have mentioned their ages in their wills, but that information isn't quoted.
Mary waited an unusually long time to marry her first husband, unless she had another husband before Atkinson who wasn’t recorded and didn’t give her any children. I see that the family tree in Geni has been adjusted so that Thomas Jr is now the brother of John Atkinson instead of his father, and William Gwaltney is now the son of Thomas Gwaltney and an unknown first wife.
One fly in this ointment is that the Gwaltney family website at http://gwaltney.faithweb.com/beginnings.html says “Around 1655, Thomas and Martha conceived a child, William, who was to carry on the Gwaltney name.” I don’t know where they got this information. They’re not sure whether the couple had a daughter or not, so it doesn’t sound like they have an original document like a family bible listing the birth. All the information on the site seems to be public records that are endlessly cited on the internet.
The timeline as I understand it:
1618 Birth of Mary Martha in England
1648
Mary is Age 30
Marriage of Mary Martha Pittman to Thomas Atkinson
Surry County , Virginia, United States
1648
Mary is Age 30
Birth of Thomas Atkinson, Jr.
Surry County , Virginia
Thomas would be 18 years old in 1666, the year Mary married Pittman
1652
Mary is Age 34
Birth of John Atkinson, Sr.
Surry County, Virginia, United States
John would be 14 in 1666
1656
Mary is Age 38
Birth of James Atkinson, Sr.
Surry County, Virginia
James would be 10 in 1666
1656
Mary is Age 38
Marriage of Mary Martha Pittman to Thomas Gwaltney.
Surry County, Virginia, United States
That’s a fast turnaround between being widowed and remarried, but if she had three young children she needed help. Englishwomen were scarce in the colonies so Gwaltney might not have minded the baggage that came with her.
1666
Mary Age 48
Marriage of Mary Martha to Thomas Pittman
Surry, Virginia, USA
1679
Age 61
Death of Mary Martha
Surry County, Virginia Colony