

According to the book "Britain's Royal Families" by Alison Weir, Henry's second wife was Adeilza. Their children were 1. William, 2. Reyner, 3. Henry, 4. Geoffrey, 5. Alice (d.1188): she married firstly John,Count of Eu, Lord of Hastings (d.1170), and had issue. Shemarried secondly Alvred de St. Martin (d. after 1189), 6. Olivia, 7. Agatha. Alison Weir also lists 12 children of Henry by unknown mothers including an "Alice or Aline; she married Matthew de Montmorenci, Constable of France, and had issue.
@Arthur, that's interesting as the Medlands site says this:
William of Newburgh records the second marriage of King Henry I and "filiam ducis Lotharingie", noting that the marriage was childless[118]. I now note that they also under William d'Aubigny that he (as second husband )and Adelisa had children: Agnes, William, Regner, Henry, Godefroi, ALICE, Olivia and Agatha.
Of Alice it says The primary source which confirms her second marriage has not yet been identified. m firstly JEAN I Comte d'Eu Lord of Hastings, son of HENRI Comte d'Eu & his wife --- (-1170). m secondly ALFRED de Saint-Martin, son of --- (-after 20 Nov 1189[33]).
I wonder if anyone has access to the primary sources....