1 night in Rotterdam...

If you like very modern cities with a little bit of night life, yes, it's worth it. If you like your cities old and pretty, than perhaps consider staying near the airport.

Are you saying that you're sleeping in Rotterdam and flying from Schiphol airport at 10AM? That sounds impossible to me.
Although I prefer The Hague, with Delft and Kinderdijk very nearby, you can't exhaust the area in one day. Note that the world-famous Mauritshuis (art) Museum in the Hague is completely closed for renovation for years. Some of their art may be on display across town. There is plenty of modern art in Rotterdam. I would like to have seen the Delta Works tidal barrier nearby, but couldn't spare the driving time.

You need enough time to get to the Storm Surge Barrier, but the Maeslantkering near Hoek van Holland is also impressive and in more easy reach - public transport - from Rotterdam.
It has a visitor centre and they organize guided tours. For, also English info see: www.keringhuis.nl

For the mills of Kinderdijk you can go to there with the Waterbus, to my unpleasant surprise their website has no info in English, so the ticket booth has to inform you.
A visit to the former oceanliner ss Rotterdam is special, it's also a hotel.

So I'm planning to spend 1 night in Rotterdam, strictly to fly out of The Hague airport the following morning. So is Rotterdam worth seeing, or should we just relax in a hotel near The Hague airport??

It’s about your preferences, Rotterdam is a modern city and becomes more and more the place for modern architecture. Boijmans van Beuningen is there a well-known museum with an international reputation. You can do easily from Rotterdam daytrips to Delft (Vermeer, Delfts Blue) or The Hague if you like more the typical old style Dutch towns, what is actually already suggested by others. We can help you better if you tell more about your preferences.

As long as you have laid out your transit to the airport for good arrival time and security, lines to check-in, etc., you'd be crazy to sit at an airport hotel. As noted, those interested in Modern Architecture might choose Rotterdam, those interested in Royal Palaces and older fine-art on the walls might select The Hague. It makes a difference how much daylight you have after arriving from Amsterdam, but Delft and Kinderdijk are both top-level attractions on Rick or Abercrombie and Kent trips!

We hope you already saw Haarlem, Leiden, and/or Utrecht as daytrips from Amsterdam. Are you there during Keukenhof weeks? It's all on the way to Rotterdam. BTW, there is a single, big tide gate in Rotterdam-proper, which I only got to see from the highway.

An interesting activity is to have dinner at the restaurant on the Euromast observation tower. Especially at sunset. You can have a clear 360-degree view of the city, the river Maas and the surroundings.