Couple options. First, the lack-of-divinity option. It is hard to ascribe divinity to someone with living offspring (and even assuming divinity was not ascribed to Jesus by the apostles, but by 2nd or 3rd generation of converts, living human family is hard to write away). In this case, I see it mainly staying as a Jewish reforming movement, which ironically, would probably be more successful, since there would be a focus on the message and not the messianic/prophetically foretold/divine aspect. There is, of course, the Paul question - I'm still unsure as to what to presume. Let's say Paul, drawn to the more radical aspect of Jesus' message, still stays the same. Can Christianity occur without a divine Christ? I'd say yes - but with belief in Jesus as Supreme Prophet, a la Muhammed. Same Pauline message of salvation through faith, but in a single God, not through Jesus. The theology and soteriology will be changed beyond recognition (and I'm too tired to come up with plausible ones at the moment...)
Divinity of Jesus retained - I think we'd see a more mainstreaming of Nestorian-esque Christology. That Jesus was fully human until the Crucifixion, then he became divine. Or that he always had divine will, and assumed divine status post-mortem. Something that makes it ok for Jesus to have kids as human, and then be considered Divine post-facto.