Separately, I like Branwen and Rhiannon. Though I'm not particularly inclined to use them, I would love to see them in a birth announcement. However, when used together and side-by-side, the names are a little too Welsh and a little too mythological for my tastes, and it ends up looking like you're trying too hard. Also, River Branwen Rhiannon is a tongue-twister of a combo. River Branwen Rhiannon=Sarah sells seashells by the seashore. Plus, Branwen and Rhiannon rhyme in a most uncomplimentary way.
As for a namesake for Rachel and Ann...I can see where you would be honouring an Ann, but it's a little too far-fetched to use Rhiannon to honour a Rachel.