[quote SunbathingDragon]@lyralalala but as things stand if/when Charles becomes King he would have custody of Prince George, not William or Kate, so why wouldn’t that power transfer to the regent?[/quote]
I've no idea why it doesn't, but it doesn't.
Guardianship, &c. of Sovereign during Regency.
During a Regency, unless Parliament otherwise determines,—
(a)if the Sovereign is under the age of eighteen years, and unmarried, His mother, if she is living, shall have the guardianship of His person;
(b)if the Sovereign, being married, is under the age of eighteen years or has been declared under this Act to be incapable for the time being of performing the royal functions, the wife or husband of the Sovereign, if of full age, shall have the guardianship of the person of the Sovereign;
(c)the Regent shall, save in the cases aforesaid, have the guardianship of the person of the Sovereign; and the property of the Sovereign, except any private property which in accordance with the terms of any trust affecting it to be administered by some other person, shall be administered by the Regent.
The Regent only has custody if the mother of a child is not around. If she is she has custody and is in charge of personal care of the child. The Regent is in charge of royal duties on their behalf.
The legal guardianship of the person of the monarch (with the corresponding power to administer the private property of the sovereign) does not necessarily rest with the regent. However, if the none of the prospective guardians provided for in the statute exist, then, also according to the statute, the regent becomes the guardian of the sovereign. Accordingly, during a regency, the regent is the person invested with the royal authority, that discharges the royal functions on behalf of the monarch. The guardian, on the other hand, has the legal custody of the sovereign (who is either a minor or an incapacitated person) and the duty to care for the monarch's personal well being. The two roles may or may not be combined.
According to section 5 of the Regency Act 1937,[14] if the monarch is under the age of eighteen years and unmarried, then his or her mother, if living, shall have the guardianship of the monarch's person. On the other hand, if the sovereign is married, but is still under the age of eighteen years, or if the sovereign is a married adult, but has been declared incapable for the time being of performing the royal functions, then the wife or husband of the sovereign, if of full age, shall have the guardianship of the person of the monarch. In all other cases except the two situations described above (that is, if the sovereign is unmarried and under the age of eighteen years, but his mother is no longer living; or if the sovereign is married, but the wife or husband is not of full age; or if the sovereign has been declared incapable of performing the royal functions, but does not have a wife or husband), then the regent shall be the legal guardian of the monarch and shall have custody of his or her person, and the property of the sovereign, except any private property which in accordance with the terms of any trust affecting it is to be administered by some other person, shall be administered by the regent.
So Kate would be guardian and have custody, but not be Regent unless parliament decreed it.
And if the Queen was incapacitated Charles would be her Regent, but Philip would be her guardian. Which makes sense.