There are varying reports on this. At QS locations, you may be asked to show ID, but some are saying you can get two alcoholic drinks per ID, so you might be able to. Some are saying they aren't being carded at all, so you would definitely be able to if that happens. At TS places, you can always ask, but I haven't seen any reports where people got more than their one drink at a TS place.
Still, if you are able to do this at every meal, you and DH will be drinking 4 alcoholic drinks each, every day. Not really passing judgment, but whew! That's a lot.