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In my experiance there is an event where one of your children asks you to join the citadel, but i think that is more or less random.
There is another posibility i have not fully tested yet but i think you can choose any maester at the citadel or the archmaester himself and let him educate the child. Try send them a gift if the refuse. At least it happend once with my second born who got the trait "maester education" (+1 learning). However due to the unfortunate early death of his older brother I called him back to my court before he finished his education.
 
I chuckled when my genius bastard son, with 18 learning when he asked for Maester education, never became a maester. He had the maester education modifier forever.