Well, it depends what Buddhism means to the parents, doesn't it?

If it's a cultural thing, then it makes sense to teach it to the kids, just like they learn to be polite and to wash their hands before eating and so on. This is how culture gets passed on. Broadening this out from the family context to the community context, that would include things like community meetings on observance days and so on, and instruction of the children by some sort of teacher or clergy or whatever. This would be the same pattern as in other religions, and have roughly the same good and bad sides. If we want to be cultural, religious Buddhists, this is obviously the way to go.

If it's the personal thing of one parent (or even both), the situation is different, but it's really just a more general case of the situation where one partner is into something the other one isn't - whether football or pottery or the great spiritual quest - only now it involves three or more people, some not fully grown yet, in a family. Here it's obviously a question of finding a good, graceful balance, avoiding toxic evangelism and indoctrination on one hand, and a lack of interest/isolation from the other family members (who are not into Buddhism) on the other hand. But kids are naturally curious and want to understand the forces shaping their lives. If one of the forces is a parent's interest in Buddhism, it's only fair to answer questions and let them know about it, even to arrange formal instruction if appropriate. There are no patent solutions to this, of course.

Here's my own angle, coming from my atheist outlook: Let the kids know all about the religions (and anything else, of course), they are interested in, encourage their curiosity but don't make a forced study of it. Tell them the myths (kids love myths and stories). Tell them about dogma, and controversy - why did God drown all the (innocent) animals and grannies and babies in the Great Flood? Why did prince Siddhartha leave his newborn child and wife all alone to pursue his own happiness? These are actual questions real children will ask. Tell them about the history of the religions - the wars, the persecutions, the golden ages, the declines, the schisms, the revivals. So much of our western society is built on the smoldering ruins of religious conflict, the kids have a right to know why it's such an ugly mess they're inheriting. Don't get me wrong: it is such a mess because real, living people thought it so immensely important to uphold noble religious ideals. The kids won't understand this, unless they can really, personally see why someone would think so highly of a religious ideal as to torture someone else to death for not sharing it. And it's important to be really honest - there has been plenty of religious conflict and violence in Buddhism's history, starting as early as the story of Devadatta, for example.

Finally, which practices to teach along with the stories and myths and theology? My daughter really likes express generosity (giving gifts, donating to street musicians, filling the bird feeder in the winter...). She also likes to cultivate good will, wishing others well, remembering in the evening the times she felt good during the day and then wishing for others to feel good like that. And she enjoys relaxation techniques such as making the limbs heavy and warm, doing some kind of low-key Progressive Muscle Relaxation at bed-time or in the afternoon. In terms of the factors of the noble eightfold path, this is training in sila and samadhi she is doing. If the panna/insight/wisdom bug bites her at one point, she'll have a good foundation, regardless of the tradition or religion she will choose to explore it. If it doesn't, these are still useful skills for her teen and adult life - being able to relax the hold on possessions, and being able to relax her body and mind.

Really interesting discussion, btw. I'd like to see more descriptions of what actual parents have been actually teaching their children, or how they actually practice.

Cheers,
Florian