Some things to pay attention to while working on your tonguing.
1. Relaxation is a key. Tension will slow you down. Keeping your tongue as relaxed as possible can be difficult to learn. I'll give you some tips in a moment.
2. Let your tongue almost bounce off the air stream rather than trying to start the air stream with the tongue.
3. Use Carmine Caruso's suggestion and form a "ts" attack instead of a "tu" or "ta" attack. This is only for the actual point of attack, of course. Drop the tongue to the "AW" position after the "ts" attack.
4. Practice first on straight single notes in all ranges (ie., 16 16th notes on G, A, B, C, etc.). Once you get the atack down this way with relaxation, then work on moving tones. Tongue some lip flexibilities, for example. Then start working on coordinating fingers and tongue. Clarke is good for the last; so is Vizzutti, Arban or even the piece you're trying so diligently to master.
Now, relaxation tips.
1. Start whispering "tsaw, tsaw,
tsaw, tsaw" over and over again as quarter notes at MM = 96.
a. make sure your jaw is positioned exactly as when you play.
b. place the second knuckle of your index finger (you pick the hand; second knuckle from the tip) on your chin where the base of the roots of your lower teeth join the jaw below the lower lip.
c. press the tip of your thumb up under your jaw below where your tongue is. Feel for tension and work to press it away.
d. continue whispering "tsaw" and feel for tension. If there is some try to massage it away while continuing to "tsaw". If it stays, slow the metronome down until you can do it without tension. Then slowly speed up. (If you find the tension-free speed you can quickly increase you capacity; if you haven't found it, it can take a long time to develop
e. Repeat on the horn after you've started to get the hang of it. By that I mean you have done it at the speed you're going to use on the horn at least 1,000 times.
2. Play 16ths on the horn at 4-12 beats slower than
the on trumpet speed from the previous exercise. Do 2 bars for each
of the following:
d. tonguing with the tongue touching as far back on the roof of the mouth as possible.
e. tonguing with the tongue between the teeth.
f. tonguing with the tongue as tense as possible.
g. tonguing as if the tongue has been frozen with novocaine (as sloppy as possible)
h. without thinking about it. (Which is easier if you fill your mind with thoughts of your breathin, embouchure, posture, fingers, horn angle, everything you can)
i. now just tongue and notice how it feels.
Sorry this got so long.
Feel free to email me with questions at email@example.com.