My mastiff pup keeps biting, trainer says keep working with him, but should I rehome him for the sake of kids?

my 5 month old engllish mastiff has bit 5 times since I got him at 8 weeks, immediatly we started seeing signs of a dominate personality, especially towards the kids. Growling, snapping, and even at such a young age. He does not constantly display these behaviors. He can be fine and go for days or even weeks with no incidents and then he just snaps. Today he bit my 2 year old in the face. He was asleep on the couch and she sat down beside of him, she did not hurt him, or sit fast as to startle him, and she was not being loud. I saw it happen. I know that a dog needs its space but this is suponsed to be a family dog. I want to be able to live with him among us without worry that if a foot accidentally is stepped on or someone startles him they arent going to be injured. He will be a 200lbs dog one day! Trainer says I need to give more suppervision and more training time with the kids, but I am already doing this. Rehome, put to sleep, or keep him?