This George Villiers, 4th Viscount Grandison (1618-1699) is not well documented.
He was the second surviving son of Edward Villiers, 2nd Viscount Grandison:
William was the 3rd viscount who died without a male heir, so George became the 4th Viscount in 1659.
George was knighted in 1644, before he became Viscount Grandison. No idea why, beyond his last name being Villiers.
In 1660 George married Lady Mary Leigh, 2nd dau. (and co-heiress) of Sir Francis Leigh, Bart., created Lord Dunsmore in 1628, and Earl of Chichester in 1644, and they had two sons and two daughters.
Grandison held the office of Captain of the Yeomen of the Guard from 1662 to 1689. Today the Yeomen take care of the Tower of London, but I have no idea if that was true in the 1660's.
Grandison married, secondly, Mary Garford, daughter of Richard Garford, on 14 November 1674. They do not appear to have had any children.
The best description of the family dynamic that I've found is in a biography of his daughter-in-law, Katherine Fitzgerald, who was born in 1661 in Ireland.
George Villiers, Lord Grandison was a good looking fellow. Harrison & van Oostende Fine Art (London dealers who launched their careers by sourcing misattributed works by major artists, such as this lost autograph portrait by Peter Lely 1618-1680).
Offered for a price in the region of £45,000 the last time it was sold, it shows George Villiers, 4th Viscount Grandison, the uncle of Barbara Villiers Palmer, Countess of Castlemaine. Painted c.1668, the oil on canvas measures 2ft 6in x 2ft 1in (76 x 64cm) and has been part of various private collections.