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"to fawn" roughly means : "to do a servile display of affection in order to gain favour"
From that, one can imagine a similar word except that the display of affection comes from a position of power (imperious). (Whether such word implies that the display of affection is to gain favour or not is irrelevant for the purpose of this question.)
e.g. Parents ought not fawn over their children but rather [do imperious display of affection] over them.
Is there a word? Or should we invent it?
I cannot think of a single word for the whole concept you are after, but I think grace comes very close
Bring honour or credit to (someone or something) by one's attendance or participation.
So in your example sentence, I would say:
Parents ought not fawn over their children but rather grace them with their affection.
If I say (unironically) that someone "graced me with their presence", I am to some extent fawning, which therefore implies that gracing is the opposite.
