I think your 2 year old should be okay. We took dd on KS on her 2nd birthday and it was one of the highlights of our trip. It is a little bumpy, but we just hold onto her tightly. She doesn't like to sit very long, we can rarely eat at sit down restaurants with her, but we just kept pointing out all of the animals and talking to her about the safari and she was fine. I have never heard about the no lap-sitting rule, as we have been to AK about 10 times in the past few months and dd has always sat on our laps to get a better view of the savannahs.