Cracroft's Peerage lists the following children for William Seymour 2nd Duke of Somerset and Frances Devereaux:
children by second wife
1. Lord William Seymour, styled Lord Beauchamp (b. 1621; bur.v.p. 16 Jun 1642)
2. Lord Robert Seymour, styled Lord Beauchamp (b. 1622; bur.v.p. 30 Jan 1645/6)
3. Lord Henry Seymour, styled Lord Beauchamp (b. c.1626; d.v.p. 30 May 1645), mar. 28 Jun 1648 Hon Mary Capell (bapt. 16 Dec 1630; mar. (2) 17 Aug 1657 Henry [Somerset], 1st Duke of Beaufort; d. 7 Jan 1714/5), 1st dau. of Arthur [Capell], 1st Baron Capell, by his wife Elizabeth Morrison, only dau. and hrss. of Sir Charles Morrison, 1st and last Bt., of Cashiobury Park, Watford, co. Hertford, and had issue:
1a. Lord William Seymour, later 3rd Duke of Somerset
1a. Lady Elizabeth Seymour (d. 12 Jan 1696/7), mar. 31 Aug 1676 as his first wife Thomas [Bruce], 3rd Earl of Elgin, and had issue
4. Lord Edward Seymour (dvp. an infant)
5. Lord John Seymour, later 4th Duke of Somerset
1. Lady Frances Seymour (bur. s.p. 5 Jan 1680/1 in Westminster Abbey), mar. (1) 28 Oct 1652 Richard [Molyneux], 2nd Viscount Molyneux, (2) 7 May 1659 Thomas [Wriothesley], 4th Earl of Southampton, and (3) 1676 as his third wife Conyers [D'Arcy], 2nd Earl of Holderness
2. Lady Mary Seymour (d. bef. 10 Apr 1673), mar. c.1653 as his second wife Heneage [Finch], 3rd Earl of Winchilsea, and had issue
3. Lady Jane Seymour (d. 23 Nov 1679), mar. 7 May 1661 Charles [Boyle], 2nd Viscount Dungarvan, 1st son and heir ap. of Richard [Boyle], 2nd Earl of Cork, by his wife Lady Elizabeth Clifford, suo jure Baroness Clifford, only child of Henry [Clifford], 5th Earl of Cumberland, and had issue
>>> Note that there is no listing for any daughter Judith. <<<
It should further be noted that the early 1620s are a bit early for middle or other secondary names without some highly unusual family circumstance.
