Apparently I can set the quantity of the product in the cart if it has a parent and a quantity_min set.
So for instance a call like
will add in the cart 2 items "child" with the exact quantity (2).
If in the same call I specify quantity_min, the quantity is send correctly but the cart shows always quantity=1
I need to specifiy the min_quantity so that the child product can't be removed from the cart (one would have to remove its parent)