You are right, responses are pretty nasty. Ignore them if they don't help you.
"Concluded with my brother in law ordering us out of holiday home. We went and haven't spoken since. WWYD???"
Who was paying for the holiday home and where did you all go?
It sounds like your sister expects you all to dance on her the attendance she dances on her princely son. The fact you could not meet her at the beach seems to have upset her unnecessarily.
I'd have a frank chat with her. Your exclamation marks after age 6 suggest you think 4 kids of 6 (or 7) and under is too many but you say you are supportive. At the end of the day I would say it's her choice.
Her choice to pander to her son, but I would say it is not a child's choice to make.
Was she trapped behind the door accidently! If not, don't hide behind a door if you will be surprised by what you hear.
Kicking you out on your mother's 80th. Your sister husband needs to apologuise big time.
This sounds like about a lot more than a missed walk on the beach.
Talk to your sis and clear the air. In future, if this could happen again, I'd not share a holiday home with your BIL - total, unnecessary over reaction on his part.