I'm also interested in this thread as my daughter will be coming up to 2yrs very soon. So far, I haven't taught her "dharma" as such, but she has naturally picked things up without any encouragement. She likes to sit with me in front of my shrine, and she hits the bell and the wooden fish and "chants". She also bows everytime she sees a Buddha which is really cute and she tries to copy the gassho mudra. If I forget to bow she tells me off and make sure I bow too!
She also says (or tries to) "Itadakimasu
" before we eat! I never shut the door when I'm meditating, I let her come in and watch me or sit with me, it doesn't bother me. Of course, I try to pick the times when she is either occupied or asleep, but sometimes you take whatever time your can get!
I'd like her to learn to meditate as she gets older, as I believe it'll be very beneficial, but I don't expect her to come along to our sangha or chant etc. I think it should be her choice to actually follow Buddhism and not something I've imposed. At the moment I'm trying to teach her how to share and not to kill any bug that she sees! Amongst the usual toddler things like not to bite, slap, scream etc etc.
I think, my advice thus far as a "new" Buddhist parent would be to not loose your temper but use energy in your voice when telling off, and don't be afraid to tell off and punish your child. Set clear boundaries. Spend as much free time with your child as possible, both individually and as a couple. Also let your child have their own time to themselves. I'm sure my thoughts and ideas will change as we both grow....