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I read this in the mid-1980's and so my memory is a bit sketchy.
In the first book, there is some environmental disaster that's coming up, but the government doesn't want anyone know, so they put the scientists that are aware of the problem on a generation ship and send them to colonize a new world. But really the government is just trying to get rid of them.
In the second book, they get to their world, but it turns out to not be that great. Something about the atmosphere being too thick. They decide to head out to a new planet.
In the third book, for some reason, only the kids remain on the ship and they've formed a quasi-religion based on the instruction video that was left for them. The main antagonist was a sneaky kid that was confined to a wheelchair. There was also an issue of the main character wanted to fix the broken things on the ship, but it was against their religion.