Internet connection doesn't have much to do with it really. Slow connection issues would appear as longer load times between holes and during the initial startup. Files are only cached between shots and between holes, but not during your actual swing. No information is transferred during the swing itself (unless you've turned on the background loading option that is normally defaulted to off).
You can check out your system specifications to make they meet or exceed our basic System Requirements. For some folks the issue lies in the inability to get a good frame rate (screen redraws) and that would appear as a general slowdown across the board (but would affect the meter as well). If you notice slowdowns in all areas, it's likely a frame rate issue and that can be somewhat alleviated by trying a few of the performance tips on my profile. Lowering the graphics quality to Medium or Low seems to help the most for players like yourself.
What are your system specs?