Well I think that's about as close as we're likely to get on this one.
The ship in the third and also the most recent picture is indeed HMS Birkenhead, one of the first iron hulled ships built for the Royal Navy. She was finished in 1845 and originally named the Vulcan, but in 1848 she was renamed the Birkenhead. She was indeed built by Laird and sons, and yes that is a caricture of John Laird. The renamed ship has special significance for Laird because his shipyard was (and via Cammell Laird who's logo you correctly identified still was until recently) in the town of Birkenhead. Birkenhead owes much of it's prosperity and development to Laird who eventually became it's MP. He was Scottish by birth though as I said, and did build the Alabama for the Confederate States of America.
Back to the ship itself though. In 1852 she left Portsmouth bound for the Kaffir Wars in Africa, transporting soldiers and their wives. She stayed briefly in Queenstown (now Cobh) Ireland and Cape Town in South Africa before sailing for Algoa Bay at all speed. Unfortunately at 2am on 26th February she struck a rock off Danger Point and more than 100 men were drowned almost instantly when water flooded into the troopdeck were they slept. The survivors were gathered on deck as if on parade and soon 60 had volunteered for the dangerous task of manning the pumps. The ship was obviously sinking so Captain Salmond ordered the boats launched. Unfortunately poor maintenance meant only three were able to be launched and were packed with the Women and Children.
Salmond then ordered that every man should try to save himself by jumping overboard and swimming for the boats. The senior officer present, Leutenant-Colonel Seaton saw that this would swamp the boats and instead ordered the men to stay put on the ship. Despite being mostly raw recruits the men obeyed his orders and didn't move even when the main mast crashed to the deck. The ship sank within 25 minutes and most of those onboard either drowned or were caught by sharks before help arrived the next day. Of 638 people on board around 193 are thought to have survived.
The term "Women and Children First" derives from this event in honour of the sacrifice made by the soldiers to ensure that the Women and Children survived the disaster, mostly at the cost of their own lives.
And the link to Frederich IV?
He was said to have been so impressed with the bravery and obediance of the soldiers that he ordered the story be read to every regiment in his army as an example of discipline and courage.