In changeable weather, you can occupy the margin between inside and out.
In general, young children are so interested in what they're doing that they don't notice the weather. Once you've got them into splash-suits or something similar, you can take them for a stroll in the park or woods and let them get wet and muddy collecting leaves or jumping in puddles, and enjoying whatever the weather throws at them.
Visits to farm shop cafés or garden centres can be absorbing pursuits during changeable weather. And if you have a garden or greenhouse at home, you may want to take advantage of the occasional cover while you tend your plants. Hardy outdoor plants love mixed weather and they'll grow fast in a combination of rain and sunshine. However, weeds love it too, so a spot of gentle clearing may be in order.
Relaxing with a book, listening to the radio or watching TV in a conservatory or gazebo gives you the best of both worlds: it looks like you're outside, feels like you're inside. The natural light makes it a great place for children's puzzles or games, too. Perhaps you can all pile in there and chill out together.