Not sure what Keukenhof "festival" you mean... This is the link to the website -- http://www.keukenhof.nl/en/. And this is the link to the events -- http://www.keukenhof.nl/en/discover-the-park/events/.
IMHO, the Flower Parade is the biggest event 25 April (http://www.keukenhof.nl/en/discover-the-park/events/flower-parade/). But perhaps you mean the Shanty Choirs Festival, 14-17 May (http://www.keukenhof.nl/en/discover-the-park/events/shanty-choirs-festival/).
In 2013 we stayed in Leiden, drove to the parade area, easily parked and watched the parade on Saturday. Wanting to miss the hoards that weekend, we didn't go back to the Gardens until the following Monday, again in our car. But we did drive around the area to see the fields and loved our visit to the Molen de Valk (http://molendevalk.leiden.nl/en/homepage/). The kids might like it better than the adults, but look closely at the pictures in this posting I did on it -- http://travelswithtrout.blogspot.com/2013/08/benelux-april-2013-molen-de-valk.html -- especially the ones of the "stairs."
My husband insisted that I do a posting of our drive from our B&B to the Gardens and back, so here's a link -- http://travelswithtrout.blogspot.com/2013/07/benelux-april-2013-driving-to-and-from.html -- to it. You are welcome to explore any of the other postings that might interest you. Click on the pictures to see them bigger, or only them.
I do think driving is the best thing to do. I also think that 2 days (3 nights?) won't give you much time to do a whole lot. The Gardens themselves can take a whole day. By the way, I drove up there from Nuremberg when I lived in Germany and camped for my first visit to Keukenhof. It was well worth the trip, but I was by myself. Your group will likely see things at a much slower pace than I did that first time or than my husband and I did 2 years ago.
Where you stay may be determined by your budget. Three adults and three kids are a lot of people. We stayed at the Huys van Leyden (http://www.huysvanleyden.nl/eng/home-english.html), but it might not be appropriate for you. Booking.com (http://www.booking.com/) can be a good resource for finding lodgings in the area for all of you. Be sure to click on "more options" in the "Guests" box to get to a place to put in the number of adults and kids and the ages of the kids. The ages can affect the types and prices of lodgings that come up in the results.
I probably have too many links in this response, but I hope they are a help and not a bother. Assuming good weather, and even without it, you will have a great time.