The double stroke you're referring to is normal, the pedal is only doing it's job and want to return in it's initial position, but your foot's on the way causing the second unwanted stroke, it's the control of the strokes/movements of your foot which causes the flutter action when you hit the batter head, it can happen with either techniques, burying the beater or playing on the rebound, using heel-down, heel-up or heel-toe with your foot.
You can avoid this by studying, analyzing and developing your movement and motion in regard to the pedal natural's action.
Also a lot can done by adjusting your pedal accordingly, your problem could be that the beater is too near the batter head, or the footplate of the pedal is set too high, or the spring is set to high increasing the speed of the return of the pedal.
Take time to adjust your pedal and/or your position behind the kit, you should be able to play your bass drum with control, accuracy, dynamics and feel without having a mind blowing experience to achieve it, it should be an effortless and a natural experience, like with you hands holding sticks, so you can concentrate in playing music, not concentrate and being distracted by bass drum flutters.
I've put a link below to give you some tips on how to get the setting working for you
I'm gonna self promote myself here, lol... http://www.drummerworld.com/forums/s...ad.php?t=93800
The OP post deal with a (working) method of how to go about about setting the pedal and the drummer to achieve what you want while using your
Yes Madge, it does mean having a hole in the reso head, typically a 4" port hole, it reduces the amount of air inside the bass drum by projecting it out, resulting in less rebound from the batter head and a dryer more punchy sound from the bass drum, it's also useful for micing purposes.