LOL at those activities!As I mentioned elsewhere, I wouldn't want my sister taking my kids on the Iraqi Adventure Tour or to the Horn of Africa to watch al-Qaeda train, but then again, I trust her to have the sense not choose dangerous activities as entertainment.
Although I'm sure very few of us would take our kids (or anyone else's) on those trips, the thing is, we all have different comfort levels and different opinions on what might be dangerous. Someone used skydiving and bungee-jumping in the same context as your examples. But are they really that much more dangerous than swimming? I am no expert and just did a super quick google to come up with some rates of death in these activities. Fatal drownings were 1.6 per 100,000 population. Parachuting 1.4 deaths per 100,000 landings. Bungee jumping .2 deaths per 100,000 jumps. Drownings are listed by popluation, but I'm sure the number of people who never swim is balanced out by the people who go 10 or 20 or 50 times a year, to get you to the 100,000 population equaling at least that many swimming sessions.
So, anyway based on those numbers, I suppose everyone here is also perfectly fine letting their sibling take their 6yo bungee jumping? As I said, we all have different comfort levels with different activities. Some draw the line at skydiving, some at trips to war-torn countries, some at a drive out of town, a hotel stay and a day at a waterpark.
If I was watching someone else's child and they told me "no artificial sweeteners", "no PG-13 movies" or any one of a million little seemingly harmless things, I'd comply with their wishes. I can't believe how many people would take such offense to a parent making their wishes known. Can you imagine asking your babysitting sibling not to show the kids a particular movie, and having her response be "well, if you don't trust me enough to pick out a movie for my niece, you must not trust me enough to watch her at all, so why don't you just stay home with her yourself!"??
For all the people who call the OP's sister "overprotective", what many of them suggest is a HUGE overreaction. The OP would be wise not to throw such a hissy fit about following her sister's wishes and just take the kids on a fun close-to-home outing, as she herself already suggested.
. They have access to my kids almost any other weekend they would want them and they choose THAT weekend to have a big adventure?

Where did the OP say she was going to disrespect the parents' wishes? And if they have a "lack of trust", as you put it, then why let her keep the kids at all?