Is there anything to support such an opinion? From what I gather, Japan is a country with a strong "nuclear family" tradition, at least as compared to the West today - even then, the "nuclear family" is the ideal in the West still. There are two ways in which a family usually differs from a "nuclear family" - either single parenthood, or relatives being more in the picture, living with the child(ren).

People still view single parenthood as a certified bad thing. Perhaps you could say that Japanese families are less nuclear because there are more relatives in the picture (I don't know if that's true) but unless that had an uptick at the same time as child suicides, there seems no basis for your suspicion, or even any reason - why would having more relatives in the picture increase suicide?