We are planning a trip to the Netherlands with the kids in the spring. We have been to Amsterdam before as a couple but this time we want to see more of the country which is said to be one of the best for family travel.
We would like to spend a few days in Amsterdam before renting a car and exploring the rest of the country. To rent the car we would not like to travel all the way back to the airport but we would need a place that is convenient to get to with children.
I've seen there are car rental places at Dam Square and out in Amstel business park.
Anyone have any advice about the best option?

I would really recommend going back to Schiphol or to maybe Haarlem to pick up a car.
Schiphol puts you straight on the motorway system to get away from the area. Driving out of the centre of Amsterdam, especially from Dam Square, is not for the faint hearted. Even getting to or out of the Amstel Business park will be tricky.

Where are you thinking of visiting in the Netherlands?

I rented a car from Hertz near the Vondelpark and returned it to Schiphol. It was not difficult leaving the city, as you are already outside the old centre.

Watch out for the speed cameras. I came home to two tickets as a momento of my vacation!

We are thinking of one day to see the flowers, one day around ZaanSchaans and Volnedam and/or maybe drive up to around Texel, one day to the Dolphinarium and maybe one of the castles, and a day in Efteling.

Ditto hetismij. Getting back to Schiphol is easy, much easier than driving out of Amsterdam. Reserve your car ahead. Get Michelin maps. This will make it easy to return the car when you fly out also.

If you can squeeze them in I recommend Madurodam in the Hague for a few hours and Duinrell in Wassenaar (just north of the Hague) for an afternoon and evening for the kids, and the kid in you.

Thanks for the great advice.
It looks like our flight back will be in the late evening so it would be best to have the car after hotel check-out and return it to the airport.

If you are going to the Dolfinarium can I suggest you stop at Muiderslot on the way, and maybe Naarden on the way back if you aren't too tired by then.
If you are AAA members you can get a discount at the Dolfinarium and the Efteling by showing your membership card.
I haven't looked to see where else you can get the discount but it always pays to ask!