There are 2 grandstands on the south of the track, both completely covered and shady. One stand on the East is uncovered. Finding a seat today was a joke. It was packed. We got there about 1:30. People were standing right along the fence line as well. If I could do it over, I would bring my own chairs and sit right in front of the grandstands (still be shaded) on the gravel. Some people were there with chairs, so I assume they will let you take them in.. but they could have been in as racers??
However, being that low the view might be a bit restricted.
If you are there earlier than us you could get a good seat I'm sure. We had 3 small children also.
The track is clear at the west end of the park, so be prepared to walk a ways. The shuttles will take you out there as well, but we had the stroller. After the final race the shuttles didn't start picking up until we had almost made it back to the entrance.