Well, Anne Standish has probably got the wrong maiden name (Clifton).
From the 4 references for Sir Cuthbert Halsall, MP , Anne & Henry Halsall do not seem to be Cuthbert's parents.
Here are some references I have found, the dates vary, I don't think some are much help. I will post them on the relevant profiles.
History, genealogical and biographical, of the Molyneux families
https://archive.org/details/historygenealogic00moly
http://www.archive.org/stream/historygenealogic00moly#page/44/mode/1up
17—109. Sir William Molyneux, a great commander in the Co. Lancaster; b. 1433, d. 1548. William Molyneux led a considerable force to serve in 1513, under his cousin Sir Richard Stanley at Flodden Field, where he took with his own hand two Scottish banners and the Earl of Huntley's arms. For this service he was personally thanked in a letter by Henry VIII. Sir William brought a considerable strength to the seasonable succor of the Duke of Norfolk, with whom he performed signal service at the battle of Flodden Field. He married Jane, dau. to Sir Richard Rugge (sometimes Rugg, — Riggs) of Rugg, in Co. Stafford; m. 2d, Elizabeth, dau. of Cuthbert Clifton, in Lanc. ; widow of Sir Richard Heskeith, Knight of Ruf-
http://www.archive.org/stream/historygenealogic00moly#page/45/mode/1up
ford, in Co. Lanc., and became in consequence Lord of Clifton. Sir William was a gallant Knight in the reign of Henry III, and displayed great bravery. On his death-bed he gave this advice to his son, "Let the underwood grow ; the tenants are the support of the family, and the commonality are the strength of a kingdom. Improve this fairly; but force not violently either your bounds or your rents above your fathers. He died 1548 and was buried at Sefton Church, where there is a monument and a eulogistic Latin inscription to his memory. Knighted at Flodden Field in 1513 and given a tiger passant proper on a crown or, for his crest.
Letter to Sir William Molyneux, Junior Knight, from King Henry VIII : .... etc.
http://www.archive.org/stream/historygenealogic00moly#page/46/mode/1up
Issue by 1st wife:
18—122. Sir Richard Molyneux, knighted at the accession of Mary, 1553; m. 1st, Elenor, dau. of Alexander Radcliff; m. 2d, Elinor, dau. of Robert Maghill ; d. 1569.
123. Jane; m. Richard Bold, Lanc., Esq. ; m. 2d, Richard Molyneux, who d. 1578.
124. Anne; m. Alexander Standish, of Standish Hall, Knt., 1518.
Issue by 2d wife:
125. William Molyneux.
126. Thomas.
127. Anne, m. Henry Halsall, Esq. of Halsall.
Sir William Molyneux, Lord of Sefton Manor1
M, #33254, b. 1481, d. 16 March 1548
Father Sir Thomas Molyneux b. c 1445, d. 12 Jul 1483
Mother Anne Dutton d. 22 Oct 1520
Sir William Molyneux, Lord of Sefton Manor married Jane Rugge, daughter of Sir Richard Rugge. Sir William Molyneux, Lord of Sefton Manor was born in 1481 at of Sefton, Lancashire, England. He died on 16 March 1548.
Family Jane Rugge
Children
Anne Molyneux+ b. c 1500
Sir Richard Molyneux+ b. c 1510, d. 3 Jan 1569
From: http://our-royal-titled-noble-and-commoner-ancestors.com/p1107.htm#...
Sir William Molyneux
Birth: 1481
Death: 1548
Family links:
Spouse:
Jane Rugge Molyneux (1481 - 1521)*
Burial: Sefton Parish Churchyard, Sefton, Metropolitan Borough of Sefton, Merseyside, England
Find A Grave Memorial# 126746049
From: http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=126746049
Dictionary of national biography, Volume 38 By Sir Leslie Stephen, Sir Sidney Lee
http://books.google.com/books?id=vAgqAAAAYAAJ&pg=PA134&lpg=...
https://archive.org/details/dictionaryofnati38stepuoft
https://archive.org/stream/dictionaryofnati38stepuoft#page/134/mode...
Sir William Molyneux (1483-1548), son of Sir Thomas, by his wife Anne, daughter and coheir of Sir Thomas Dutton, led a considerable force to serve in 1513 under his cousin Sir Edward Stanley at Flodden Field, where he took with his own hands two Scottish banners and the Earl of Huntly's arms; for this service he was personally thanked in a letter by Henry VIII. He joined Derby's Salley expedition in 1536 (GAIRDNER, Letters and Papers, ii. 1251), and died in 1548, aged 65, being buried in Sefton Church, where there is a monument and eulogistic Latin inscription to his memory. He was twice married, and his son Richard by his first wife, Jane, only daughter and heir of Richard Rydge or Rugge of Ridge, Shropshire, was knighted at Mary's accession in 1553, served as sheriff of Lancashire in 1566, and died in 1569. He also was twice married, and by his first wife, Eleanor, daughter of Sir Alexander Radcliffe, was father of William, who predeceased him in 1567, and grandfather of Richard Molyneux created baronet in 1611, who was father of Richard first viscount Maryborough .... etc.
SEE ALSO https://en.wikisource.org/wiki/Molyneux,_Richard_(d.1459)_(DNB00)
'A genealogical and heraldic history of the commoners of Great Britain and Ireland enjoying territorial possessions or high official rank, but uninvested with heritable honours Vol. 2 by Burke, John, 1787-1848
https://archive.org/details/heraldichistory02burk
https://archive.org/stream/heraldichistory02burk#page/55/mode/1up
CLIFTON, OF CLIFTON AND LYTHAM.
.... etc.
THOMAS CLIFTON, whose name appears in the list of the retinue of King Henry V. into France, in 1415, which terminated by the battle of Agincourt, 25th October, 1415. (Nicolas, p. 278.) He settled lands in Goosnargh and Wood Plumpton, upon his son, James, on his marriage with Mar-
https://archive.org/stream/heraldichistory02burk#page/56/mode/1up
garet, daughter of Sir Richard Huddlestone, of Millum Castle, in the county of Cumberland, knt. who died in the lifetime of his father, without issue, on the 8th September, 1419. Thomas Clifton died in 1442, leaving by his wife, Agnes, daughter of Sir Richard Molyneux, of Sephton, knt. a son, his successor,
RICHARD CLIFTON, who on the 4th October, 21st Henry VI. 1442, paid forty shillings to Thomas de Latham, receiver of the rents of the Duchy of Lancaster, on obtaining livery of his lands in Clifton, Westby Field, Plumpton, Salwyk, and Barton. In 1460, he settled lands in Salwyk on his son James. He m. Alice Butler, daughter of John Butler, of Rawcliffe, in the county of Lancaster, and had issue, James Clifton, who m. Alice, daughter and heir of James Lancaster, of ___ in the county of Westmoreland, 1st March, 36th Henry VI. A.D. 1457. He d. 6th HENRY VII. A.D. 1490, (Inq. P.M.) and was succeeded by his son,
ROBERT CLIFTON, who m. Margaret, daughter of Nicholas Butler, of Bewsey, in the county of Lancaster, by whom he had two sons,
CUTHBERT, his successor.
WILLIAM, who in 1516, on the division of the estates of his elder brother, Cuthbert Clifton, who died without male issue, by the award of Justice Brudenell and Serjeant Palmes, had the manor of Wortley, and its dependancies, allotted to him. This gentleman will be found carrying on the male line of the family.
The elder son and heir,
CUTHBERT CLIFTON, of Clifton, m. Alice, daughter and co-heir of Sir John Lawrence, of Ashton, in the county of Lancaster, knt. By deed of November, 18th HENRY VII. A.D. 1502, he settled his estates upon himself for life, and to his issue male, with remainder to his brother, William. He d. in 1512, leaving an only daughter,
ELIZABETH, who m. first, Sir Richard Hesketh, knt. of Rufford, in the county of Lancaster, but had no issue by that gentleman, who died in 1520. She wedded secondly, Sir William Molyneux, knt. of Sephton, who became in consequence, Lord of Clifton. By Sir William, who died in July, 1548, she had an only daughter,
ANNE MOLYNEUX, who espoused Henry Halsall, esq. of the county of Lancaster, and conferred upon him the Lordship of Clifton, which remained with his descendants until it again merged in the Clifton family, by the marriage of Anne Halsall, daughter of Sir Cuthbert Halsall, with Thomas Clifton, of Westby.
Cuthbert's younger brother and continuator of the male line,
WILLIAM CLIFTON, of Westby, m. Isabell, daughter of — Thornborough, .... etc.