... or at least she's never mentioned that...

It's the Andorans, especially the political players, she doesn't want to know she's the lover of the Dragon Reborn.

That would have cost her the throne if they knew, and now it would still be political poison as she'd look like a devious snake after making a show of her independence from the Dragon, to announce she's bearing his children...

There are also too many people (not just the Shadow, also political rivals, people like the WC and probably even foreign rulers) who would seek to assassinate those children if they knew they were the Dragon's. It's one hell of a legacy for them to bear. The way Rand is perceived by the people will have to change a lot for Elayne to afford to reveal publicly the heir of Andor is the daughter of the Dragon Reborn. If Rand dies, it's quite possible Elayne remains single (the way the Andoran system works, it's her motherhood which is proof of legitimacy - she never has to reveal who the father is. He could be an Ebou Dari beggar that Elayne's girl would still have full right to inherit the Throne...)


It's not such an issue with Mat, as you've forgotten that it's too early still for Elayne's pregnancy to be showing (especially in the kind of dresses WOT women wear). She would have the opportunity to forewarn him not to mention Rand publicly before any audience (Renee could whisper it to him as she brings him to Elayne, etc.)