Not that I disagree with this or the rest of your explanation, but I still think that Elayne should have told Rand. She has many reasons not to since it is first politically difficult to approach the dragon, second dangerous to her children if it is found out, third she is extremely busy, and fourth Rand is very busy himself.

But, there is one overwhelming reason to tell Rand and that is because it is his right to know. Elayne was raised without a father with a nurse that was in many ways her true parent. But even with the best nurses and Elayne's attentions the babies still need a father that is involved from the beginning.

I don't know how Rand would have respond, but neither did Elayne and she did not even try.