Traveling in Iceland with kids is absolutely no problem. Iceland is a very kid friendly country and many tours are perfect for kids as well.
Icelanders include their kids in everything. Some restaurants for example will have an area where kids can play and it is usually no problem to add a baby crib to a room. And many towns will have a playground for kids with a "bouncy hill" they can jump on.
And there are many fun activities that kids can enjoy as well. In this itinerary I've made a list of all the fun things kids can join in on. It is not like a regular itinerary because you can not do all of these things in one day, but you will have a list to choose from.
