It sounds like PILs were being very stressy and anxious to get to the event in time. You sound equally stressy about them and their reactions. You need to calm down. I feel sorry for your DH and friend stuck in the middle of this.
It sounds your PILs are very particular and regimented and you are a bit chaotic. They are not going to change, particularly if they've invited you to a very formal black tie event. Of course people like that will want to leave early.
You played right into this. Its rubbish blame it on the traffic when you only live 15 mins drive away in normal conditions. You know the area. It sounds like you just left 15 mins to get there and came unstuck as a result. It wasn't the same as being a bit late for a casual gathering at their house.
If you wanted a quieter life with less petty nagging, You should have bombproofed the event as much as possible when you know what their triggers are.
As for finishing getting ready there. Never do that, it is just going to add to the chaos and allow them to open fire.
My Pils are just like this and can quickly escalate into headless chickens over minor details. But they see it as rude not to be on time and they see it as a lack of respect not to make the effort.
I've learnt through painful experience to make sure I prepare well in advance if I want to avoid the fall out.
Also the Tux/DH's Friend/ MILs comments can all be discounted. Why are you so worked up about it? Its DH's job to assert himself here. She could hardly expect the friend to take off the tux, although it might have been quite funny to see her face if he did.
In conclusion just stop!!
Its all so minor and could have been anticipated and avoided.
You know what to expect next time so prepare for it and try to remain calm, you will then have the upper hand and find them much easier to deal with if you do.