Last winter, during our first trip to FL, we visited several different areas. Since I too am a Detroit Tiger fan and wanted to see a spring game we found a campground in Winter Haven called Cypress Campground & RV Park. They have 194 sites and I'd guess that more than half were pull-throughs. It was a nice park with gate security and right next to a Wal-Mart. Click on their website below. Also, it's very near the old Cypress Gardens, now called Lego Land.
http://www.cypresscampground.com/The other clicky below is from RV Park Reviews.com listing the rated campgrounds in Lakeland. If you've never used this site be sure to check the ratings by different campers as well as their comments. You can also find campground websites from the clicky.
http://www.rvparkreviews.com/regions/Florida/Lakeland.html