You really should go to the track to watch!
I assume he is doing the actual driving experience (not just the ride-a-long) since you are looking for things to do & that requires more time.
Sleep in while he goes over & gets registered & trained (he can make other arrangements to get there & then you can drive over). Then, take the kids & enjoy the "show." They will drive the family around the track in a van (pretty quickly I might add) & show you what it is like.
They really do it up & I am sure your husband would be grateful to have a cheering section for him when he's up. They make a pretty big deal of it at the WDW track.
My kids were just 3 & 1 when my DH did the driving experience & they enjoyed watching their dad drive the fast car. They still remember it now, 3 years later.
You can also video & take photos to document his achievement.
Also, he will get done early enough that you can enjoy the rest of the day with family plans -- whether that is Downtown Disney or swimming or whatever.