William (b. 1600- d.1670s/1680s) married Joann Dancer on Feb. 29, 1627 in Little Horwood. He was a blacksmith as was his father William Sr who died in Little Horwood in 1650 (I have a copy of his will that I can share with you).
As far his son Robert Sr. and grandson Robert Jr., I assumed they married in Winslow or Cublington and that the records simply were incomplete. In speaking with some of individuals running winslow-history.org.uk, they verified the parish records in the 1670's and 1680's were incomplete. I think this explanation might be more likely an answer then an out of county marriage. However, that doesn't mean it wouldn't be a good idea to check!
Both William the elder and his son William went by the surname Paladie/Palladine at times in addition to Paradine. William the elder was likely the child of Henry Paladie/Palladine/Paradine who lived in Swanbourne in the 1570s
In regard to Thomas (1708-1759), it appears he had A LOT of children although almost all of them did not survive into adulthood. His first wife Margaret died in 1743 after giving birth to twins (who also passed away). He then married Elizabeth. In all, out of 13 children, I can find evidence of only one reaching adulthood. His youngest son William Paradine married in Aylesbury 29 Apr 1778 to Elizabeth Seamons. They settled in Weedon for a time before moving to Great Kimble.
There are burial records for some of Thomas's other children, and other deaths can be inferred by the fact that multiple children are baptized with the same name. However, that does leave the door open for Robert (b. 1749), Thomas (b. 1751), and John (b. 1753). I can find no evidence that they survived however. Thomas Sr. died in 1759 and Elizabeth Thorn remarried Edward Baker in 1760.
Curiously, there is ANOTHER William Paradine who married a Mary Scott in Puttenam, Hertford. He would have likely been born in the 1750's and almost certainly came from this line of Paradine's... could he have been a son of Thomas Sr? Perhaps, this William was baptized by a different name (?) but took on his father's name? Or perhaps he could be the son of an unknown child of Robert Paradine of Cublington? This of course is just speculation, but a Y-DNA analysis could help prove the connection.