Okay yeah, what I mentioned will solve the problem of the armscye gaping open. Also, did the armscye fit snugly -before- you attached the trim? If it didn't, you'll need to remove the excess to further reduce that gappage.
The neck is a bit trickier because it's not a solid ring. Because it's open in the front, you don't have any tension across the front of the neck to hold it in place or keep the collar straight up.
Also, think in terms of fabric recoil: when you stretch a knit, it wants to return to its original shape. The shortest distance to do so is a straight line. That's probably why your collar points are turning down and everything's pulling away from your neck.
My thought is to break up the direction of the trim fabric at the collar corners and the center of the front neck. You also might want to initially pattern the neck so that it's more closed to begin with, allowing it to gap on your neck just by virtue of the fabric's natural pull. Of course, this is stuff you'd have to experiment with, since I'm not able to physically handle your fabric.
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