Hi there, Nonnie!
Ooooh, this may be a convoluted answer. Here we go!
Here’s my Aelir tag, so you can get a handle on who she was. I’ll separate this answer out into each of the princes, so you can get the gist of their relationships.
Laindawar
When he was born, Aelir often bundled her eldest child onto her back as she raced through her beloved woods. Laindawar grew to toddlerhood sitting under green eaves beside his mother, or strapped to her as she clambered and danced and leaped through the trees.
Aelir was an odd sort of duck. She was tall, dishevelled, nearly squirrelish in her manner, not very talkative at all. Her eyes spoke more than she did. She was more at home with her trees than in the company of other elves, and Laindawar most definitely absorbed this tendency. He too is a loner more content under the branches. This is not only due to his own natural tendencies, but to those early formative years spent with his mother, alone but for the wind in the leaves and the soft puff of their breath.
As he grew, Laindawar was brought forward into the world of his father: the court, the business of being a crown prince and a political figure. He would retreat to his mother as an escape, for the peace and rest her presence brought.
(Thranduil did likewise, funnily enough. Aelir was a calm, wild haven for them both.)
As Aelir sickened, Laindawar’s resolve to kill all the evil in the forests hardened into something diamond-plated and implacable. He has never given up.
Laerophen
Our awkward giraffe was born several years after his brother, and he was at one glance obviously Thranduil’s child. He had the hair, the eyes, the height! Yet he was in spirit a retiring soul, and preferred the quiet and his own company.
Also, it appeared that he was made mostly of elbows and knees.
It was for Laerophen’s sake that Aelir began to stay longer and more frequently in the palace. It was Thranduil who taught him to read, but it was Aelir who sat with him and listened as he devoured all the books around him and told her about what he had learned in excited piping tones.
She often brought him out of his rooms, just the two of them (three, if Laindawar were willing to take time away from his hunting). Unlike Laindawar and Legolas, Laerophen would walk through the trees by his mother’s side. He would not leap from bough to bough. She would hold his hand.
She taught him the bow, though he did not show any especial gift for it. But he loved the time with his mother, and so he worked diligently at it.
When she left, Laerophen’s world contracted to his rooms once again. The only one who could coax him out was Legolas.
Legolas
Their little green leaf was such a shock. SUCH A SHOCK. Aelir had been sickening for centuries – how was she to know that this was any different? But there it was, she was due another child. Weakened as she was due to the poisoning of the forests, she worried. God, did she worry.
She needn’t have worried, not for him. Legolas was walking before he was crawling, desperate to stand and do everything right now!! NOW!!! He wanted to see everything, know everything, touch everything. He was, unlike her quiet eldest children, noisy. He cried loudly, sang loudly, laughed loudly.
He was effusively affectionate.
Everything in him bubbled over with curiosity and joy.
Aelir brought him into her forests as much as she was able, and strapped him to her back as she had for Laindawar. Unlike his brother, Legolas did not enjoy being confined to such safety. As soon as he was able, he wriggled free to dangle and clamber and run just as his mother did. “Look Naneth! Look at me! Look what I can do!”
He made her laugh helplessly and happily, even as the shadows under her eyes deepened.
She tried to stay for him. She truly did.
