If you can not do the sitting trot without stirrups, that means you rely on your stirrups too much. You know what that means? Better start practicing no stirrups!! The biggest thing that will help with a sitting trot and to ride with no stirrups is to RELAX. Part of the reason why you can't ride with out stirrups or sit the trot is because you are probably very tense and nervous. You feel this way because you know what happens when you sit the trot. The only thing to fear is fear itself.
The sitting trot can be one the most beautiful things ever when done correctly and you and your horse are moving as one.
When you are preparing to sit the trot take a deep breath, let it out, sit and relax. Focus on how your horse moves and how he moves you. Breathe. Loosen up in your hips and allow him to move you. Breathe. If it gets to be too much, start posting and once you've regained your confidence, gently come back to the saddle. Breathe. ;)
Lunge lessons would also be great right now. Then you can concentrate on all of this and not worry about where he's going.