I do actually have some empathy for you. I can see how it would have happened,
You want to join in with your husband and kids. This is totally normal.
But as responsible parents neither of you should have ignored the weight limit knowing you were over. You could have hurt one of the kids.
Once you're in, it's hard to stand up and get off. Causing disappointment and embarrassment, I can see why you'd maybe just stay seated and hope for the best.
I think you're upset and embarrassed about it, so you're looking for someone to blame, to make someone pay. It's easier than saying " what the hell was I thinking"
But there is a personal responsibility here. The park cannot be more at fault than you and your husband willfully ignoring the weight limit and you knowing you were struggling and not saying anything, especially not with your kids impacted.
If they had said something, would you have got off? If they had said are you sure you're all within the 315, would you have said, no we are not, so we shall leave, sorry kids, or would you have said yes, and got on anyway?
What is it you hope to gain? Do you want the park to start to ask seriously overweight people their weight? To sign disclaimers? To weigh them? That the sign isn't enough? They need to also be asked? For staff to be able to look at them and make a judgement because they can't be sure they will do it themselves?
You won't get financial recompense, but I would think about what you're trying to achieve here.