'... it was in the interest of ...to suggest to the ... public ...' ? . . .

LEO: Siehe Wörterbuch: Interesse liegen . . .

Tja, suggest liegt nahe, das ist aber zu schwach als Gegenstück zu "suggerieren". Die Frage ist, ob der deutsche Text eine Rücküberestzung aus dem englischen "to suggest" ist. Wenn nicht, paßt es, wie gesagt, nicht ganz.

Perhaps as alternatives:
... the government was interested to influence the public's idea of the perfect family.
... the government had an interest in influencing the public's idea of the perfect family.

Q: Could one render "suggerieren" with "manipulate the public's idea/view", or is that going too far?

... eher nicht - wie wäre 'to shape'? . . .

I am with Steve: "manipulate the public's view" is what the sentence suggests.

Yes, "shape" is probably what I was looking for. How about this:

...the government had an interest in shaping the public's view of the ideal family.

Edit: On the other hand, if "manipulate" works:
...the government had an interest in manipulating the public's view of the ideal family.

"Manipulate" sounds quite a lot more hostile than "shape".

suggerieren is hostile.

... seid ihr etwa mit Vicky Leeks befreundet ? . . . ;-))