These sites are great, thanks. I have found a few articles by searching for the ship "Broadaxe"
1. Arrived: brig Broadaxe, 120 ds frm Port Adelaide via Pitcairn's Inland; Source: California Digital Newspaper Collection > Sacramento Transcript > 5 August 1850
2. 7 March 1851 "Board of Health vs. John Lambert, master or brig Broadaxe — Judgment in favor of plaintiff tor $35,900" ?? he was going by the name of Lambert instead of Lamb.
3. 1852 Attempted Murder: apparently the Broadaxe was attacked by the crew of the Chilean Brig Porvenir and they attempted to stab the Captain and his daughter. Daily Alta California, Volume 3, Number 74, 15 March 1852
By the looks of it the family could have been living and trading on the Broadaxe.
cheers Janine