The problem is that you are not moving the yarn forward and back appropriately so as to avoid wrapping up the back side sts, which are being slipped, as you create the nose on the front side.
When working a front st the yarn can be held in front to purl or back to knit. When slipping a back st the yarn needs to be held in front of the back stitch (i.e.between the front and back pieces). If you leave the yarn in back it will end up on the outside of the piece (i.e. rs of the back), making it visible from the outside and interlocking your two sides.
Before doing the WTS you need to make sure to slip the prior back st wyif before wrapping the next front st, then turning and working your way back.
If you are having trouble, you may find that temporarily separating the back and front stitches while you work the nose may help. Slip all the front stitches onto a needle placing the back sts on a holder. Follow the pattern to work the nose (using only the front stitches). When done place all of the stitches back on a single needle (alternating front and back) and resume your double knitting.
Here is a post I did elsewhere about a similar problem.
Hope this helps.