I don't think the Queen was obliged to entertain "America," as the two countries have a special relationship and she is friends with the American Ambassador Will Farish (having stayed at his home in Versailles, KY.) Moreover, she is also contact with former President Bush and his wife ...
As for funerals, weddings, etc ... I recently did a bit of research and checked the news coverage for weddings and funerals for the entire 20Century. It has been customary for the British sovereign to send a rep to a wedding or a funeral. Queen Elizabeth II's presence at the funeral of King Baudouin was most unusual and rare. British sovereigns appear not to attend such events. I went as far back as Frederik VIII's funeral (Denmark).
The sovereign has sent children, siblings, cousins, uncles, even, relatives by marriage, to represent him or her at royal weddings and funerals. In 1947, KIng George VI sent the Duke of Beaufort, who was married to a cousin, to represent him at the funerals of Christian X of Greece and George II of the Hellenes (who died a few weeks apart.)
Iraq had nothing to do with the British not attending Laurent's wedding ... it was unlikely that the sovereign would send a rep to the wedding of a younger son - as they barely know Laurent's generation.