My FIL is an advanced diabetic, I've known him for 20 years and he has never had an anger outburst because of his diabetes. Never have I heard that diabetes causes anger outbursts. Never. Completely untrue.
OM is flat out lying to her and that's a hard position for YOU to be in. I would not be ok with my kids being around a man like that and I would make that boundary known. If he can't keep his health on track to mitigate his so-called "diabetes induced outbursts" then perhaps he needs an in-home nurse.