Poor service indeed. Presumably child was on KL1072 leaving Manchester at 0600 arriving Amsterdam at 0830, connecting to KL 661 departing at 1030 for Houston, which was missed. I only say this because the times quoted are at variance.
Indeed there are two further flights that day to Houston, another KLM at 1425 and a Continental (supposedly KLM's SkyTeam partner) leaving at 1545. An Unaccompanied Minor potentially being stranded overnight would have expected to get priority on these.
But at the risk of stirring things may I ask :
Did you choose KLM for the trip because they were the cheapest fare ? In this world you normally get what you pay for.
Is it appropriate for a child making such a journey who needs an escort to be routed via a third country connecting point, especially at a city which is a well known centre of vice. If she has this escort need could someone not have taken her to Gatwick and put her on a direct BA or CO flight. many airlines now will not accept transfer UMs because of the problems that can and do happen at the transfer point.
Do bear in mind that in international travel problems happen and everyone has to be prepared for them.
In summary though quite inappropriate and you may like to call through the press for the Chief Executive Officer of KLM, Mr Leo van Wijk, to account for his company's cheeseparing actions that led to this.