Honestly I would be surprised if this is a health issue. It seems to be circumstantial.
You need to put a bubble of respect around the children. Through the dog's respect for you he needs to respect the kids. By putting a bubble of respect around the kids you are keeping the kids safe and helping the dog feel safe. You are taking charge.
As the dog becomes more comfortable around the children, then you can make the bubble smaller as the dog starts to calm down. Right now that bubble should be at least a few feet from the children.
If the dog growls at the kids in your presence (and the dog should only be with the kids if you are present), then you give a firm "no", use your leash to remove him from the kids and the area in general. He is not permitted to claim the space or aggress towards the children. You claim both the space and the kids. Let him know with your energy, eyes and attitude that you are not happy. You might even have to shuffle towards him as you back him out of the area.
But then you have to recreate the situation until he learns to remain calm in their presence. Don't push his comfort level too far or he will get snarky again. Stay at sub-threshold with the kids. Do not expect him to get too close at first. You just want him to feel comfortable within a reasonable range of the children. Let him stay there, pet him, reward him and wait until he takes a deep breath. Signs of acceptance and relaxation are sighing, sitting voluntarily, or laying down voluntarily. When he is relaxed let him know that is the answer with your warm tone, soft touch and relaxed smile. This is a good time to end this session.
This is a system of pressure and release. Pressure for the wrong choice and release the pressure & reward for the good choice. Dogs understand this naturally as it is how they communicate with each other. Though the truth is dogs don't really reward each other - they don't go out and grab a mouse to hand to the other dog. The simple release of pressure and returning to good times is sufficient. The key is to always end on a positive note. A common mistake is the dog makes a bad choice, the person corrects the bad choice and they quit, and the dog never learns what the acceptable choice is. They end on failure. In this case success is no growling or snapping, and a relaxed, calm attitude.
Love Them & Lead Them,
~Elizabeth & Doug
Dog Training the Way Nature Intended