There seems to be no evidence supporting the idea of these van den Haaks being the parents of leutenant Didrik Henrik Haak/Hake. A somewhat similar surname or his alleged birth in Livonia (Livland; an area that included parts of the present Estonia and Latvia) is hardly enough. There were several other Haaks/Hakes (without van den) in that area and also in the neighbouring countries.
Pekka Vihervuori