Your husbands military background may give him certain views about life and about what it means to be a man, and those views will certainly be challenged if he has PTSD ("I should be able to just deal with this because I'm strong..."). It's ok for him to want your child to grow up to be "strong" and to be neat and tidy but you're talking about a 3 year old - they need nurture and care, to be messy and loud and adventurous. And to be taught how to express their feelings, to understand that it's ok to feel scared, or angry or hurt and to know how to express that.
For example, if your child did grow up and join the military - he's a long way from being in an emergency where his tidiness would make a difference to his survival and the military would teach him all he needed to know anyway. So, at 3 years old, he had a long way to go.
If I were you I'd separate out his parenting and treatment of your child from his PTSD and set clear boundaries about what is and isn't ok in terms of discipline, chores etc. Your son is very little, too little to be expected to "man up" and too little to keep military standards of tidiness. It sounds like you know it isn't ok for him to be so hard on your little boy, calling it a symptom of PTSD just masks what can be a fairly common issue in military families, and is actually mistreatment.
For example, if your child did grow up and join the military - he's a long way from being in an emergency where his tidiness would make a difference to his survival and the military would teach him all he needed to know anyway. So, at 3 years old, he had a long way to go.
If I were you I'd separate out his parenting and treatment of your child from his PTSD and set clear boundaries about what is and isn't ok in terms of discipline, chores etc. Your son is very little, too little to be expected to "man up" and too little to keep military standards of tidiness. It sounds like you know it isn't ok for him to be so hard on your little boy, calling it a symptom of PTSD just masks what can be a fairly common issue in military families, and is actually mistreatment.