Oh, I don't think you implied that mama. :) I was replying to some of the people who replied to your OP; not to your OP directly.
I don't think your DS was being disrespectful.
Disobedient, sure, but you can't expect obedience from a 4yo without properly beating or coercing them into it. If anyone was disrespectful it was the grandparents. They should respect his limits, he is not yet able to hold the leash on his own or walk by himself safely and he needs help- not lessons about safety that he is unable to comprehend.
4 yo is an age of independence and clearly your DS feels comfortable enough in his abilty (good job mom!) to disregard the judgement of your ILs and discern for himself his own level of safety. In the situation of the dog, he had a tantrum. So what? He wanted to prove he was capable and he wasn't allowed...he got over it and apologized...what more could ASK of 4yo? In the latter as it happened your MIL was wrong, he knew the way, he knew you were just ahead, he could see you...he had a need for comfort and he met that need on his own without the permission of his grandma who clearly didn't understand when he said "I am hot and tired, I want to go home." that he meant it. The question is if they had been MILES from home and you were no where around...would he have done the same?
Your ILs need respect, sure, but they also need to respect him and his needs. Rather than take the leash off of your DS your FIL could have helped hold it. Rather than dismiss the needs of your DS your MIL could have phoned your cell and asked you to wait up because DS had changed his mind and wanted to go back.
I think you can expect a 4 yo to listen to rules and follow them IF the rules make sense and take into account their needs, abilities, skills and knowledge...not when they are randomly imposed without consideration for these things.
I think you're doing a good job with him!
I really, really, really don't like the way people throw around the words "respect" and "disrespect." Most people equate those words with "obedient" or "disobedient" when it comes to children. I don't think that an occasionally disobedient young child is being disrespectful; a 4yo simply lacks the ability to control strong emotions. A 4yo has trouble rationalizing that adults might know what's best for him.
People who say that's "disrespectful" are making the issue about themselves rather than about the child. It's egocentric.
I don't think your son was being disrespectful. I think he was overwhelmed with emotion in the first scenario and handled it poorly....you know....because he's 4. In the second scenario, it sounds like your MIL was making him stay with her for no other reason than that she could. I think that is disrespectful of the child.