Jimbo,
Haven't posted in here for years, but do look reasonable regularly. I noticed this on Harewood, which is the closest motor sport venue to me and around 20 minutes away. I go once or twice and a year.
You shouldn't have any issues there with children. I went on various occasions as a child and have taken/take my daughter, when she was little and as a now teenager. I've also taken my nephews when they were younger.
Car park is right next to the paddock. With children you possible need to keep an eye out for cars moving around the paddock, but by and large it's not like some venues where there is a lot more going on and moving and you need to have eyes in the back of your head with little ones.
Facilities are decent but if you do walk down to the farmhouse bend, which is the best spot for me, it's a bit of climb back up for little legs!
Take clothing for all weather as no shelter whatsoever. Same at the vast majority of motor sports venue, but you are particularly exposed at Harewood as you are on the side of a hill. Toilets there and there is usually a guy selling coffees and cakes, an ice cream van and a burger truck.
Have fun!
Andy