The DNB gives this - I think I can quote this much without infringing copyright:
On 30 August 1718 he married Elizabeth Barrel at Barrow upon Humber; she died on 18 May 1726, and on 23 November that year he married Elizabeth Scott at Hampstead, Middlesex. She died in 1777. Two sons, John (1719–1738) and William (1728–1815), survived infancy.
No mention of Alice. DNB has no mentions of a relevant Frodsham - the only one is Bridge Frodsham, actor, 1734–1768.
The book is Longitude (1996) by Dava Sobel, an excellent read -I'm afraid I can't locate my copy. There is also a more recent paperback edition as well as a Kindle version.