First: your children can travel the trains almost free with the so-called Railrunner ticket. EUR 2,50 for the whole day.
The OV Chipkaart, available at railway stations, is only practical if you will also be using bus, tram and/or metro. But it will cost you EUR 7,50 for the card, needs a minimum balance of EUR 20 to be able to use it on the train (EUR 10 for bus, tram and metro), and you only get the unused balance returned at the railway station when it doesn't exceed EUR 30. I'd say buying separate tickets will be the more economical way. But make sure you have a working bank card when using bus or tram: they don't take cash anymore. (Both Amsterdam and The Hague have day tickets for the local transport, with special prices for children. Amsterdam is EUR 8,50/4,00; the Hague EUR 7,10/1,50.)
As noted above, distances are short, if not minimal, and there is no real reason for changing hotels. With your children Amsterdam might not be the best play to stay. Try Haarlem or Leiden, both manageable smaller and less crowded cities with a lot to see and do, and everything within walking distance.
There is also no need to have your first and last night at Schiphol airport, unless your flights arrive and depart at ungodly hours. From Amsterdam, Haarlem and Leiden the airport can be reached within half an hour on very frequent public transport, or even with a taxi without breaking the bank.
I am wondering why your children choose Noordwijk for a beach. It is awkward to reach (bus from Leiden) and not the most lively place. Scheveningen is much better and easily combined with a trip to The Hague proper, only a tram ride away.
Added:
There is one place which justifies a change of hotels: Dordrecht. The city itself is rewarding as a historical river port city and for all the river traffic around, but also a good base for the windmills of Kinderdijk, and the way to reach them with the river ferry Waterbus. The Waterbus continues to Rotterdam, which makes it a nice long day out (provided the weather is co-operating).
