Our stay in Alicudi has been a great experience for us. We stayed at the house with our children aged 4 and 5 and had a memorable week together. This is certainly not your usual holiday house. The state of the house is probably best described as artful decay with very basic comfort. It is like stationary camping de luxe with a marvelous view.
To enjoy the place with little kids it is advisable to come prepared and with the right mindset: Of course there is hardly anything to do on the island, but much to see and experience. And it is not easy to get to. We travelled by plane, train, ferry and eventually mule. But the calm and quietness of the island reward that effort.
If you are thinking about travelling there with little kids, we can certainyl recommend it. Our kids managed the daily 20 minutes steep walk to the beach and shop well. There is enough space on the terrace to play. What maybe needs to be kept in mind though, is that it gets really hot in the summer (at the beginning of June we already had more than 30 degrees) and the terrace is well in the sun until 15.00, so you may have to spend some time in the house until the afternoon because the 1,5 hour steep hike further up the hill in the heat is a bit too much for the little ones. Plus the beach consists of dark rocks which get really hot and make it hard to for the kids to walk into the sea. Also your kids should not be the fearsome kind, as there are insects and geckos in the house.
Michaela is a great help upon arrival, gives a good introduction to the house and lets you know how the infracstructure of the island works, to make for a smooth start.
Give it a try, it is nice adventure for the family!