Going to an amusement park while pregnant?

We (my husband, my parents, and my two children) are planning on going to an amusement park in a few weeks. I am about 13 weeks pregnant, and I obviously know that I can not ride any of the "thrill rides" (roller coasters and such), but should it be okay to ride the kiddie rides (for example, they have a train that goes about 5 mph on a track that curves around the amusement park.)? I know they have roller coasters for kids and stuff, but I am not even talking about those. Basically, I would like to ride some rides that my 2 year old son will be riding (just so I am not stuck standing around, and so that I can get a little breeze on a hot day!) Should this be okay?