Well, the story seems to have progressed a bit. First, we didn't know the deluxe nature of the trip, then OP admitted to contemplating having her daughter conspire (her words) with the friend to get the other parents to pay for it without them ever even mentioning it. Now we see that the friend's family has already taken OP's daughter on an all expense vacation to Maine, including airfare.
I think it's rude to invite a kid on a trip and expect any kind of payment from the parents. As many people have stated, it puts the parents in a bad spot if they, like most people, don't have spare money lying around. It very likely will affect their own family vacation. And the OP admitted that she was, in fact, considering having the kids essentially put those parents in that position, which is, well, let's just say "not very nice".
Given the additional information regarding what this family has done for her daughter, I find it pretty unbelievable that anyone would consider putting those parents in that spot after what they have done. Especially since the primary reason the OP can't afford to add the friend is because they are willingly going on a super-deluxe trip and aren't willing to tone it down in order to bring the friend with them.
I didn't realize there was a conspiracy. In that effect, I'm a bit speechless.
Again, I as the parent would expect to pay for my own child. But, then again, as a parent asking, I would also be prepared that it couldn't happen.
This could really be tricky. Very tricky. Apparently the OP has made it even worse by discussing this with the daughter's friend before talking to the parents first.
The simplest thing in this case is to go to the parents without mentioning a word to the daughter or friend. period. If nothing else, this should be done out of respect to the other family.
Hopefully if I'm ever put in the position of asking a friend of the family to go, I would have the wherewithal to do as I've suggested above.
Additionally, you'd probably want to ask yourself if this trip is a gift to your family or your daughter. For my b'day many years ago my parents surprised me by asking a friend to go with us to DW. We were 16 at the time. They dropped us off on multiple days and let us do our thing. Was a great time. I believe my folks covered nearly all of it, but my friend has his spending money. Granted the flight was free and the hotel was, too (my father traveled a LOT and racked up many points in this time). Having said that, if this is a gift for the daughter, then IMO the friend's fees should be encompassed. I don't believe it's wrong to ask the other family for help, but in this situation you're essentially asking another family to buy your child a gift. That's just not right.
Guess I don't have much else to say. The OP has likely tied her own hands if she has truly 'conspired'.