I need your help

Yes, first of all rule out pain or illness. Does he seem dominant most of the time or just when you scratch him in a certain place? Growling at him does not make you dominant. Things like making sure he is not on the furniture or bed or anyplace he can get above you to look down on you and making sure he gets nothing in life (food, treats, play, affection) without working for it will make you a benevolent pack leader. Growling is strictly for puppies to be able to communicate with them affectively while they are young and still learning. It is the easiest way and still fresh in their minds that when Mommy says GRRRR I stop what I am doing. Dogs that are a bit older will need to be taught in a different way. How old is Caesar? Is the aggressiveness all the time? with everyone or just certain people? How old was he when he came to you? Do you know if he was with his mother long enough to learn bite inhibition (8-9 weeks)?

I really hate defaming a company publically, but I have rescued an awful lot of beagles where the homes have used the same training company that you did. They seem to use harsher methods than the situations warrant and can make a sensative and trusting breed like the beagle fold. What did you call them in for and what were their recommendations?

I totally second NILF. Make him work for every bit of affection, food, treats and praise. I would even go so far as to take away the bowl and hand feed him so he has a direct visual on who is the provider of food.
Don't let him up on furniture at all, beds, couch, or anywhere else he may be able to look down at you. You go through doors first, upstairs first and eat first (which I'm sure BB told you).
You can also try associating petting with treats so he has the most positive feelings towards it. Pet him once (under the chin - very unthreatening) and if he allows this without growls give him the treat. If he does not allow make sure he knows that you and the treats are leaving the room. If he follows you great...try again. If he doesn't then perhaps the lure isn't strong enough and you should try another treat (hot dog gets em every time). Work you way up to the side of the face and then the top of the head and then back.
A few things may be contributing factors. Moving may have caused him to become less confident and more territorial. Obviously he has chosen the couch as his. Second, is he at all jealous of the child in the house? No matter what do not leave them unsupervised together. We recommend a child never be left alone with a beagle until they are maybe 6 or 7. Too many things a child does is very threatening behavior to dogs.
It is so hard to help with a problem I can't see, but this is what I would recommend for Caesar. I have seen a lot of beagles come through my house that in no way shape or form were from good breeding lines or properly bred, but none were human agressive without some provoking factor. You just have to figure out what it is. I wouldn't suggest a professional trainer as you have already had one come in. I would suggest you find a certified animal behaviorist in your area.
Good for you for recognizing the choke collar as a useless tool for a dominant beagle. Improper use of such devices can lead to worse agression problems.