No, it wouldn't be accurate to say that she was "matriarch of the Cavendishes." Her maiden name was Poyntz (da. of Stephen Poyntz). She married in 1755 John Spencer, who was created 1st Baron and Viscount Spencer in 1761 and 1st Viscount Althorp and Earl Spencer in 1765. He died in 1781, when she became the Dowager Countess Spencer. She lived from 1737 to 1814.
Two of her daughters were Georgiana Spencer (1757-1806) and Henrietta Spencer (1761-1821). Georgiana married the 5th Duke of Devonshire in 1774, and so technically became Georgiana Cavendish, but she was always known as the Duchess of Devonshire. Henrietta married the 3rd Earl of Bessborough in 1780, and was known as Lady Bessborough.
> The Duchess of Devonshire is the mother of Lady Georgiana
> Cavendish (later Viscountess Morpess), Lord Hartfield and
> Lady Harriet Cavendish (Hary-O, later Lady Granville).
Almost. Lady Georgiana Cavendish (1783-1858) married Viscount Morpeth in 1801; he later succeeded his father as 5th Earl of Carlisle, and so she was then known as Lady Carlisle.
Lady Harriet Cavendish (1785-1862) was nicknamed Harry-O; she married in 1809 Lord Granville Leveson-Gower, the son of the 1st Marquis of Stafford. He was created 1st Earl Granville in 1833.
William Spencer Cavendish, their younger brother, bore the courtesy title Marquis of Hartington during their father's lifetime, and became the 6th Duke in 1811. He never married.
> Lady Bessborough is the Mother of Lady Caroline and Frederick
> Ponsonby and the lover of Lord Granville (incidentally, by
> the time Granville married Hary-O, were they still having
> an affair? Do you know when were they married?).
I cannot be sure without re-reading my vague book about Lady Bessborough, but it appears that, while they may not have been lovers as late as 1809, they remained close and exchanged letters all their lives. However, any hope Lady Bessborough had of renewing their sexual relations ended firmly with his engagement to Harriet, whom he may not have loved as passionately, but he certainly loved as well.
> Lady Caroline Ponsonby is married to William Lamb and his brother George
> is married to Hary-O's half sister Caroline St. Jules
> (daughter of the 5th Duke of D. and Lady Elizabeth Foster -
> do you happen to know where she came by that surname?).
According to Henry Blyth in his bio of Caro Lamb: "because an accomodating French aristocrat, Comte St Jules, expressed his willingness to accept paternity for the Duke's illegitimate child."
> I don't know where to place Harry Cavendish (which is a
> cousin of the 5th Duke, but I don't know what relation he
> has with the remaining Cavendishes)
The most famous Henry Cavendish (1731-1810) was a bachelor, an eccentric recluse who was also a brilliant chemist and philosopher. He was a grandson of the 2nd Duke of Devonshire and therefore was his first cousin once removed. There was another relation named Henry Cavendish alive at that time, though: a son of George, brother of the 5th Duke (b. 1783) (whose own nephew became the 7th Duke).
> and Frederick Lamb.
William Lamb's younger brother.
> Also, there's a reference to Caroline Lamb's following in
> the steps of her mother, aunt and uncle; but I don't know
> who the uncle was and what he did.
Doesn't she just mean regarding taking lovers, in which case aunt and uncle are just the 5th Duke and Duchess of Devonshire? I don't know anything about Caro's father's siblings.