The problem that arises here is similar to star wars (although the prequels were a trainwreck); people have a memory associated with the original and now that memory was tarnished. Ron Moore was not looking to really even re-imagine, he was looking for a place to allegory real world situations and try to make viewers think; it did not always work so well because there were obvious agendas in some of them; but for the most part it worked. What does it mean to be human? What do people really do in war? If your about to become extinct and are aware of it - how would you react to a given situation? The old show was created at a time when things like just were not possible on cable and it was never intended to be a think piece series; it was and always will be a religulous view of star wars - and there is nothing wrong with that - you just shouldn't hold it against the new series because that is not what it is about. Star Trek DS9 was another good example of this departure; Moore expressly got involved in DS9 because with Gene passed away the "it always has to have a happy ending" hand cuffs were taken off. Again, many fans were angry at DS9's darkness (which compared to new BSG is lightweight) but the point was not to do yet another trek, it was to try and make people think about what war is like, what are humans really like (both the good and the bad).
In the end though, I still look at this as completely separate and not even a re-imaging. I still watch the old series on retro TV and I do not feel any sort of loss.
I do suggest for kids though try out Eureka; you might need to screen Eureka (depending on the children's age) but for the most part it is light hearted fun.