I've been pulling my 2 1/2 year old daughter for about a year in a burley trailer. I don't like bike seats because it makes the bike too top heavy, harder to control. In my head, more dangerous than the trailer. The trailer won't tip if the bike tips.

And in the trailer, the kids can carry things to keep them occupied. I don't worry about her dropping a sippy cup. That'd be sketchy to drop something on the road.

Whatever you do, make sure the kid has a helmet. I acclimated my kid by wearing the helmet during play time, so she wouldn't fear it. And, so she wouldn't associate an uncomfortable helmet w/ only bikes. It worked and it became more of a "hat". Then I wouldn't let her in the trailer w/o a helmet. Now she knows the rules.