I agree. She is definetely not the usual royal type. Good for her that she is not in that prominent position to have to represent her country. Being beautiful and rich she can pursue her own interests. She is, a rare example in royals, very intellectual, studied philosphy and much into thinking and contemplating about life and the problem of humanity. And she is a great lover of literature and reads a lot (just like me). That's one of the reasons I can connect with her. In fact I bought some of the books she recommended and wasn't disappointed.
About her private life concerning men and having children I don't know why she made the decisions she made. Does every woman know exactly why she wanted to have children?
I believe she was searching for a good relationship with a man she loved and having a good family life , but unfortunately it didin't work out for her. We don't know how Gad or Dimitri acted as husbands or fathers. Don't forget both of these men already had fathered a child and separated. It cannot be all her fault alone.
I don't think that she is a cold mother to her children, how can we know? I remember seeing pictures some time ago with her two sons, going on holiday, spending time with Dimitri's daughter from his first marriage. I was happy for her watching her relationship with Dimitri, very sad that it didn't work out for them.
She doesn't want to share pics of her children as many other prominent people don't want to. Nothing wrong with that, it is her private decision. I always had and still have a soft spot for her and don't think that she is cold, she is just more into philosophical and literture issues, which is quite unusual in royals.