As to the in-laws.....because you did give them permission to take her with them to "play".....and it was YOU who had the misunderstanding as to what exactly "playing" meant, I sort of feel like that's on you. It's not like they lied to you or anything. So i'm havign a hard time finding fault with them in this scenario. Now, if you had told them prior to this "my child is not to ride mechanical rides" and they did it anyway, that would be a WHOLE 'nuther story...but it sounds like they offerred to take their grandchildren to a fun place, they had your agreement to take the kids to the rides, at leats they "thought" they did. I think it's one of those parenting things you sort of have to learn..never ASSUME that another persons judgemnent is going to be your own. Some people have no issues with small children going on rides, some people have no issues feeding their kids McDonalds, some people have no issues having a gun in the home, some people have no issues letting uncle stan, the convicted child molester, live with them for a while and babysitting the kids while they run out ot the store. Ask, ask, ask.
As to the "park"...I would hope the staff was following proper procedure. If you have reason to believe they weren't, i think that deserves a complaint phonecall. But..it's quite possible that some of the rides truly didn't have a height restriction, or that the child met it. My eperience has been that the minimum height for small kids rides is 32-36 inches, and your child might very well be that tall.
I took dd to an amusement park for the first time when she was 10 months old. I have pics of her having a blast on little cars, boats, a tiny roller coaster, train, merry-go-round, etc. Ds first when when he was 18 months - he was not able to ride as much stuff, because he's super tiny, but he still had fun. We did however, scrupulously obey the height requirements. We've had great experiences at the 2 places we have taken our young children, the staff, even the young teens that seem to abound in those places, were always very careful about checking for height, buckling the child, or affixing the bar, etc. I would certainly be upset if they did not. As ot the bar thing...is it possible that YOU being in the car with her actually made it so the bar could not be tightened down effctively? I know I've had that happen..because I am much bigger than my children..therefore, with the bar tightened down on ME, it is extremely lose on my child, and yes, I hold on to them. BUT..if they were on alone, the bar would have been tightened down on THEM, and therefore have been much, much tighter. That might not have been the case in your situation, but it has been my personal experience.