The three girls are Canadian citizens. I presume the 1983 Hague Convention is intended to prevent children from being kidnapped from their home countries, not to prevent them from being taken from a foreign country back to their homes.
If the mother thinks she should have custody, she should return to Canada and argue the matter there, IMHO.
Regretably Canada is determined to do everything upside down: to favor LGBTs before normal people, and to favor other countries before their own. Still, this looks to me to be a twisting of the obvious intention of the Hague Convention.
This is where we get to find out if the Hague Convention trumps the Charter of Rights- specifically, the clause in the latter enshrining the right to stay in Canada.
No, it is meant to prevent one parent from running off to another country with the kids in the middle of a custody dispute. This family was legally residing in the UK at the time of their dispute. It is proper that the dispute be settled there.