it sounds like you're doing everything right so far - do you bring treats outside to treat him once he's "done his business" outdoors? i also have found it helpful to train my dogs to go on command - something i picked up from raising guiding eyes puppies - everytime he starts to go (outside, like he should), say your command (we used "get busy"), then treat. they soon equate "get busy" with going to the bathroom, and it's a nice way to get them to go when you don't feel like standing outside in your jammies for 20 minutes while your dog finds the perfect spot to pee.
i am sure you already know this, since you have another beagle, but i would highly recommend finding a basic obedience class that uses positive reinforcement to enroll him in as well - they like to be busy, beagles do, and you can often curb some of their more destructive behaviors like barking, digging, etc, by giving them something more productive to do.
good luck with your new family member!