Welcome to the forums, reggie.
It looks like you're using the same embroidery file for both the t-shirts and baseball caps. Since you're new to embroidery, I'm assuming you didn't digitize the design and you probably did not mention to your digitizer that the design will also be embroidered on baseball caps.
Basically, you should have a separate file for the caps. All you have to do is tell your digitizer that you need the design edited for caps and be sure to say what kind of caps it will be embroidered on (e.g. 5 or 6-panel, unstructured or structured, low-profile or high-profile).
Editing a design for caps involves rearranging the sequence in which design elements are embroidered. The rule of thumb is "bottom-up" and "center-out." If you have 6-panel baseball caps, the center seam is also taken into consideration and solved with generous underlay in that region.
Hooping or framing caps properly makes a huge difference on how the embroidered design will turnout. Make sure you frame caps tightly.
If you're embroidering unstructured caps, there is specialty backing you should consider called "cap backing." Cap backing is much thicker and stiffer than your everyday backing. These properties preserve the cap's shape while providing stability in the stitching process. Be sure to cut it long enough so that it is included when you clip the cap. Cap backing is also a tearway, an added bonus.
Hope that helps. Let us know how things turn out