Fair is not equal. Different aged children have different privileges. I have five children, and they can understand this. The 7 year old knows that he doesn't have a cell phone like the 13 year old because
1. He's not old enough for a cell phone and
2. The only reason the 13 year old has one is because he rides his bike to and from school and sometimes there is bad weather and he needs to call me to pick him up.
Things don't HAVE to be fair when there is a big age discrepancy.
This, of course, doesn't mean that the Fred is in charge and gets to do whatever he wants. And strictly speaking, YES, he should do whatever the OP asks of him, because she is in charge. However, having already parented a 12 year old I can tell you that going to the park with a bunch of littler kids is not even remotely his idea of a good time. The younger kids enjoy it. I don't think it's surprising at all that Fred is bored at the OP's house, he's 12. What does he have to do there that typical pre-teens enjoy? My 13 year old would be bored to tears if I dropped him off at someone's house who only had much younger children and then told him he can't get on the computer either. I'm not saying OP has to change her computer rule or even her outside rule, but I completely disagree that the rules MUST be the same for all children in order for it to be "fair". It's already not fair, the younger children are doing something they truly enjoy while the oldest one is bored out of his mind. An almost teenager is not the same as an 8 year old and shouldn't be expected to enjoy the same things.
To accomplish the goal of getting some quiet time, which I completely agree is 100% reasonable, I think the OP should talk to Fred about it. Tell him that there will be quiet time after lunch and ask him to bring a book or something for that time since he has outgrown the park. If the other kids ask, tell them Fred is older and the park isn't really designed for his age (it's not.) so he will be doing something else during that time.