now, there's still hasn't been any moment where the siblings bully her in front of him, so can you say he let's them do it? She also haven't told him so how could he know?
Her position is indeed different, for starters, shes a commoners child, so most probably she won't be taking the crown, why have her meddle with politics? He even gives her a nice place to live, in a castle besides the one where he lives, with a personal maid of her age and caretakers, if anything, they only thing he would be guilty of is lack of conversation, and because of the low chapter count as of now, that point is also something we will have to see.
He won't get close to her so easily or fast, after so many years, and even when he tested the waters it was obvious how she didn't like him, so I really don't think they will bond any time soon without a reason. and also he can't force the sibling to be loving to her, having them separated daily is a good decision in my opinion.