According to Sir Thomas More: Biography, Facts and Information and according to
The last letter of Sir Thomas More, 1535 the Act of Succession was that which began the events leading to More's execution.
It was the Act of Succession, passed the following month, that sealed his fate. It stated that all who were called upon must take an oath acknowledging Anne as Henry’s wife and their future children as legitimate heirs to the throne. This More was fully prepared to do. [Facts and Information.]
More was prepared to suffer, as a subject, the demands of Royalty. But some believe that the words added to the Act, regarding 'prince or potentate' were added specifically to entrap More :
But – and of course this clause was added simply to trap More – the Act also required a repudiation of “any foreign authority, prince or potentate.” More could recognize Anne as the crowned queen of England. But he could not recognize the king’s authority as head of the new church of England. And so he was imprisoned in the Tower of London on 17 April 1534. [Facts and Information]
More had made little comment to Henry when the King claimed his previous marriage, to Catherine of Aragon, to be 'incestuous' (and therefore should be annulled) a non-existent argument since the brother involved, Arthur, died in 1501, eight years before his widow married Henry in 1509.
Wherever Henry found scriptural backing for this argument is not clear. John the Baptist's rebuke to Herod Antipas regarding his brother Philip's wife is irrelevant since both men were alive at the time. There is far greater scriptural argument that, since the brief marriage of Catherine and Arthur was childless, Henry, the brother, should marry the widow and produce progeny.
But More was not prepared to attend the King's subsequent re-marriage to Anne Boleyn in 1533. And not prepared to swear the oath in allegiance which excluded any loyalty to a foreign, earthly, power.
Nor was More prepared to accept Henry as the 'Head' of the Church in England.
Thus, to answer the question, More felt obliged, it would seem, to resist Henry and Parliament and he was not permitted to merely be silent on his own position, privately.
The Act demanded an oath to be sworn.
But More's last letter reveals nothing about either his intentions, or his own personal view, regarding his family and their rights or their future in England (or anywhere else).
The Wikipedia entry on 'hanging drawing and quartering' explains that those being so executed for treason - as was Henry's former wife Catherine Howard, although, being a woman, she was only beheaded - would, as she did, make a submissive confession on the scaffold, not for their own sakes, but for the sake of their surviving relatives, who could well suffer the same fate if the Monarch was displeased with how matters were going with the purging of treasonable rebellion.
For whatever reason, political or personal, Henry commuted More's sentence 'hanging drawing and quartering'(the usual for treason) to a simple beheading.
Therefore it is unlikely that Sir Thomas More's intentions regarding his family's status beyond his decease would be documented. If he made provision of any kind, then he probably did so secretively and if he discovered any justification for them not being treated as he was, then it would have been unwise to publicize that information widely, at the time leading up to his own execution.