dear new rider,
Just to let you know, this that you are experiencing is very normal and very common. I remember the very same experience; only being able to sit the trot without stirrups, and as soon as I took them up again, everything falling apart. IN a way, it's just a matter of riding a lot . You kind of have to go "through" the difficulty, not around it.
What I think may be happening, is that when you are riding w/o stirrups, you may be staying on a bit more by gripping, more than you realize. Then, when you pick up the stirrup, you may still be gripping, and this will inevitably cause you to lose your stirrup..
So, when riding w/o stirrups, forget about how your feet are possitioned. think only about riding from your seatbones and letting the weight of your legs on each side of the horse be your balancers. Then, try to get a similar feeling when you pick up the stirrups.
But, to a certain extent, it just happens, and you are not alone there.
Congrats to you for doing so much work w/o stirrups. YOu'll be a good rider soon!