It certainly does look like Elizabeth Church is the wife of Thomas Vesey or Vesy of Aldham in Suffolk not Thomas Vessey of Little Baddow, Essex.
For some reason known only to Google, I couldn't access the full-text from Google Books but it is here and the original Visitation of Suffolk is here
If the baptismal dates on the Thomas Vessey profile are correct then John, Sybil, and Susan are his children with an unknown wife.
Edward Vesey and Mary Vesey are then the children of Thomas Vesey of Aldham and Elizabeth Church.
The son Thomas Vesey is interesting because the baptismal date is as of the son of Thomas Vessey of Little Baddow, but the death date is possibly that of the Thomas Vesey the son of Elizabeth Church and Thomas Vesey of Aldham.