It sounds like you might have some things to unpick about the parenting you received as a child and perhaps the way that your parents continue to interact with you. This is not unusual when we become parents... we move from seeing the best in our parents as children, to having distance during adolescence and early adulthood then when we have children, we want them to have a relationship so we often find ourselves coming closer again, having changed, while they may not have done.
When we have our own children, we reflect on how our parents were with us and compare it to the type of parents we want to be and it can bring up a host of emotions that we have suppressed or new emotions that we are faced with.
I remember my mother looking at me playing with my children, I felt very judged, but she told me I was a good mother. It felt sad because she does not feel that she was a good mother - I didn't receive the brunt of it, but my sister did. My father is a wonderful grandad, but he was not present as a Dad.
In your situation, it sounds like everyone was emotional and I think there is a lot for you to unpick. Go over it, analyse your own reactions and work out how to navigate in the future. Decide which pieces you want to address with your parents and take it from there. I would suggest, starting with sorry.. it was stressful, DS was tired and didn't want to leave. Next time, we will try to handle it better. See what their response is... you might consider asking your mother if there is anything she wants to play with DS, long before you are ready to leave and gently reminding her that before leaving, it would be best to keep things calm - it often feels like others are deliberately sabotaging our parenting, sometimes it might be unconscious, sometimes unintentional, and sometimes not.. there was one stage with my parents, I was convinced that they were deliberately hiding pieces of lego - there was a whole lot to unpick there!!
With your father - you should address this face to face, without emotion and without expecting him to apologise, he already has. Dad, I know you think I am soft and you are entitled to your opinion, but I will parent DS in the way that I see fit. I am grateful that you recognised it was not your place to touch DS in the way that you did and I would ask you to remember in future that I do not want you to discipline him in that way.
Mum, I understand that we all got over emotional and I regret that it played out the way that it did, I will do my best to ensure that it does not happen again and I would ask you to also do the same. We can talk about it, when the situation is less charged and when DS is not there. I do not want him to model calm behaviour, especially when he is struggling to regulate his own emotions.
I am a homeopath... I would offer everyone some chamomilla!!