Very late to the party - but here's what I recommend for people who might encounter similar challenges: book a LIFO (often, you can book for the same amount what is called Last In First Out) ticket. RDU - ATL and overnight (you will recover your dogs and baggage, overnight in a hotel near the airport using a hotel lister like www.dogfriendly.com) and the next day check in with all for the first flight out.

This gives you much more control and better assurance you and the dogs will be on the same flights; the tickets generally can be had for the same amount. We may do this when we have iffy flights - such as SFO-ORD-NRT, and the last time we overnight at ORD; it snowed overnight, and the sold-out ORD-NRT flight departed 1/3 full because the snow affected most connections and some people who were driving longer distances to get to the airport - or SMF-DFW-CZM.