You plan on spending from 10am to 1pm at Vander Veer? There isn't that much to do there, and it isn't that big. You will be done in less than an hour. Since you are going to be in the QC anyway, why not take the 5 minute drive to Rock Island to view the Quad Cities Botanical Center also. You will be glad you did, do both. Schuetzen park doesn't offer that much either. Why not check out the German-American Historical Museum on Gaines and 2nd Street at the foot of the Centennial Bridge between Davenport and Rock Island. For the most part all of these things could be accomplished in less than a day leaving you plenty of travel time to Dubuque which is only about an hour's drive to the north on US Highway 61, 4 lane divided highway, 65 MPH, all the way to Dubuque, where there are plenty of historic shops and Frank Lloyd Wright architecture.
It's a shame that you didn't let your readers know what all is to be seen at Schuetzen Park. The Park is a great urban wildlife park with hiking trails and picnic sites. Ther is a historic "street car pavillion" in the Park and there are cultural events held there throughout the year. Why not just enjoy the tranquility. Have you heard the phrase "stop & smell the roses"?