If this museum trip is something you really want for your child, and you think that it would make a big difference for him, I'd start out by calling or e-mailing the museum to explain the situation and asking if they know of any resources that are local to you that might provide some of the same benefits.
I'd also look into alternative methods of travel and lodging that might bring the cost down to something reasonable. Is there a reason you'd have to fly? Use your social network - do you have friends who have friends who have friends who are local to the museum or who are on the drive there who would be willing to let you stay over for a night so that your kid can have his trip? Is there cheap camping along the drive instead of staying in a hotel? Is there a possibility that you could rideshare with another family to split driving chores and fuel costs?
Think outside the box - just figuring out ways to make it happen has the potential to be a fun project for the family - but also realize that if not going to this museum is enough to kill your child's interest in the subject, it probably wasn't going to be their life's passion anyway, regardless of how interested in it they might seem now.
