Loire Valley in February

February shouldn't be too cold, but I wouldn't plan on spending more than an hour a day outside. I would try stay in the city, simply because the heating is likely to be more reliable - choose Tours, Amboise, or Loches. We're lucky down here, the days are longer than you get in London at that time of year, but it won't be balmy :)

Luckily the chateau have plenty to appeal to kids, top picks would be Chenonceau, Loches and Langeias, because there is plenty of exploring to do, and Loches lends itself to climbing towers and exploring the tunnels.

The aquarium near Amboise has a good reputation, and the swimming pool at le Lac in Tours is amazing - an olympic sized outdoor pool with a tunnel from inside the building for real swimmers, and a couple of fun kids pools including a waterslide.

On your February trip, you should make your Loire Valley base at the towns of Amboise, Chinon, or Blois. They are located near the chateaux and you can rent a car in Amboise to drive around the region.
Chinon is a nice base and less touristy. If you do choose Chinon, you might find this hotel appealing for your stay. I spent 3 nights there and the service is excellent.

http://hoteldiderot.com/en/rooms/

https://www.airbnb.com/rooms/12086086?location=Amboise%2C%20France&adults=4&children=1&check_in=2019-02-11&check_out=2019-02-16&home_collection=1&guests=1&s=HRknjlCd

https://www.airbnb.com/rooms/27164491?location=Amboise%2C%20France&adults=4&children=1&check_in=2019-02-11&check_out=2019-02-16&home_collection=1&guests=1&s=HRknjlCd

Here is another Airbnb in Amboise

https://www.airbnb.com/rooms/8250188?location=Amboise%2C%20France&adults=4&children=1&check_in=2019-02-11&check_out=2019-02-16&home_collection=1&guests=1&s=HRknjlCd

The Zoo-Parc Beauval near St-Aignan might be another kid-friendly option if you or they get "chateau-ed out." Supposed to be one of Europe's best.

Dick - very true - forgot that one!! They have baby pandas, I believe.