My dog bit my son requiring many stitches. I think this has something to do with our family structure, what are your thoughts?

Hi there, I am writing this to you in a state of high distress. My doberman who is 2, we have had him 6 months, just bit my 5 year old son requiring many stitches. This is the 2nd incident and I believe it is a dominance pack issue thing as it only happens if he is alone with my kids, something I try desperately to not have happen. I don't know what my son may have done to provoke it but it would likely have been trying to hug the dog he said he had rolled onto his back and he went to pet his stomach when he jumped on him growling and obviously biting. Are the muzzles okay to leave him in for long periods. I am looking to muzzle him whenever my kids are home and not muzzle him other times I have been training him with a remote collar system and he has gone from out of control to being able to walk off leash no problem. Even with other dogs when he starts to lunge and growl I just click the dogtra collar and he comes or sits or whatever with no dog fights it just seems to be a family "pack " issue. When we first got him he growled and snapped at me several times in a very menacing way and I was told to pinch his lip really hard and force him into a down which he did and started to tremble and rolled into a submissive posture and I have never had that problem again he is definitely my husbands dog first and mine second as I am the one who takes him for 5 -10 walks or runs.

Any way long story short I now no longer trust him and my children are far more important so can I leave him in this muzzle for large periods through the day and should I put it on him when I go out even though his main issue seems to be in our house with my kids?

This is the only option I can think of as I love him to bits and can't bear the thought of re-homing him as we are the 4th or 5th place he has been in 2 years. I just don't know if we gave him to a home without kids if it would be better or if we would be screwing him up with dumping him into yet another home.

PLEASE answer this rather long winded email if you can thank you.
Lea